Mapping the Energy Landscape of Non-Convex Optimization Problems
Zhu, Song Chun
and the corresponding ELM. The ELM of an energy landscape reveals important char- acteristics of the landscapeMapping the Energy Landscape of Non-Convex Optimization Problems Maira Pavlovskaia1 , Kewei Tu2 and Technology, ShanghaiTech University, No. 8 Building, 319 Yueyang Road, Shanghai 200031, China tukw
Convex Optimization Convex Optimization
Masci, Frank
in the United States of America by Cambridge University Press, New York http://www.cambridge.org Information published 2004 Seventh printing with corrections 2009 Printed in the United Kingdom at the University Press that preserve convexity . . . . . . . . . . . . . . . . . . . . 35 2.4 Generalized inequalities
Lavaei, Javad
. INTRODUCTION The optimal power flow (OPF) problem aims to find an optimal operating point of a power system1 Convex Relaxation for Optimal Power Flow Problem: Mesh Networks Ramtin Madani, Somayeh Sojoudi and Javad Lavaei Abstract--This paper is concerned with the optimal power flow (OPF) problem. We have
Gong, Pinghua; Zhang, Changshui; Lu, Zhaosong; Huang, Jianhua Z; Ye, Jieping
2013-01-01
Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning settings. However, solving the non-convex optimization problems associated with non-convex penalties remains a big challenge. A commonly used approach is the Multi-Stage (MS) convex relaxation (or DC programming), which relaxes the original non-convex problem to a sequence of convex problems. This approach is usually not very practical for large-scale problems because its computational cost is a multiple of solving a single convex problem. In this paper, we propose a General Iterative Shrinkage and Thresholding (GIST) algorithm to solve the nonconvex optimization problem for a large class of non-convex penalties. The GIST algorithm iteratively solves a proximal operator problem, which in turn has a closed-form solution for many commonly used penalties. At each outer iteration of the algorithm, we use a line search initialized by the Barzilai-Borwein (BB) rule that allows finding an appropriate step size quickly. The paper also presents a detailed convergence analysis of the GIST algorithm. The efficiency of the proposed algorithm is demonstrated by extensive experiments on large-scale data sets. PMID:25285330
Goodrich, Michael T.
On the Complexity of Optimization Problems for 3Dimensional Convex Polyhedra and Decision Trees and decision trees are NPhard or NPcomplete. One of the techniques we employ is a lineartime method, decision trees. 1 Introduction Convex polyhedra are fundamental geometric structures (e.g., see [20
An Exact Solution to the Transistor Sizing Problem for CMOS Circuits Using Convex Optimization
Sapatnekar, Sachin
An Exact Solution to the Transistor Sizing Problem for CMOS Circuits Using Convex Optimization topology, the delay can be controlled by varying the sizes of transistors in the circuit. Here, the size of a transistor is measured in terms of its channel width, since the channel lengths in a digital circuit
Marlin, Benjamin
Convex Functions Smooth Optimization Non-Smooth Optimization Stochastic Optimization Convex Optimization Mark Schmidt - CMPT 419/726 #12;Convex Functions Smooth Optimization Non-Smooth Optimization;Convex Functions Smooth Optimization Non-Smooth Optimization Stochastic Optimization Motivation: Why
Convex optimization methods for model reduction
Sou, Kin Cheong, 1979-
2008-01-01
Model reduction and convex optimization are prevalent in science and engineering applications. In this thesis, convex optimization solution techniques to three different model reduction problems are studied.Parameterized ...
The Optimal Solution of a Non-Convex State-Dependent LQR Problem and Its Applications
Xu, Xudan; Zhu, J. Jim; Zhang, Ping
2014-01-01
This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR) problem, in which the control penalty weighting matrix in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE) simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting . It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting , in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions. PMID:24747417
Joint Equalization and Decoding via Convex Optimization
Kim, Byung Hak
2012-07-16
The unifying theme of this dissertation is the development of new solutions for decoding and inference problems based on convex optimization methods. Th first part considers the joint detection and decoding problem for ...
An Overview Of Software For Convex Optimization
Borchers, Brian
convex, problems solved by gradient based local search methods.) · The development of interior point Shift · From the 1960's through the early 1990's, many people divided optimization in linear programming (convex, non-smooth, problems solved by the simplex method) and nonlinear programming (smooth, typically
Henrion, Didier
A review of the book "Functional analysis and applied optimization in Banach spaces - Applications to non-convex variational problems" by Fabio Botelho, Springer, Cham, Switzerland, 2014. The book extensively in the landmark book [I. Ekeland, R. Temam. Convex analysis and variational problems. Elsevier
Convex Optimization: from Real-Time Embedded
Hall, Julian
, vision networking circuit design combinatorial optimization quantum mechanics Convex Optimization 7-means, EM, auto-encoders (bi-convex) Convex Optimization 8 #12;Example -- Support vector machine data (ai
Marlin, Benjamin
Convex Functions Smooth Optimization Non-Smooth Optimization Randomized Algorithms Parallel Smooth Optimization Non-Smooth Optimization Randomized Algorithms Parallel/Distributed Optimization Smooth Optimization Non-Smooth Optimization Randomized Algorithms Parallel/Distributed Optimization
First-order Methods for Convex Optimization with Inexact Oracle
Glineur, François
Effect of inexact oracle on GM/FGM 7 Applications to other classes of convex problems Non-smooth convex optimization 4 Definition of inexact oracle 5 Examples of inexact oracles 6 Effect of inexact oracle on GM/FGM Examples of inexact oracles 6 Effect of inexact oracle on GM/FGM 7 Applications to other classes of convex
Adaptive Algorithms for Planar Convex Hull Problems
NASA Astrophysics Data System (ADS)
Ahn, Hee-Kap; Okamoto, Yoshio
We study problems in computational geometry from the viewpoint of adaptive algorithms. Adaptive algorithms have been extensively studied for the sorting problem, and in this paper we generalize the framework to geometric problems. To this end, we think of geometric problems as permutation (or rearrangement) problems of arrays, and define the "presortedness" as a distance from the input array to the desired output array. We call an algorithm adaptive if it runs faster when a given input array is closer to the desired output, and furthermore it does not make use of any information of the presortedness. As a case study, we look into the planar convex hull problem for which we discover two natural formulations as permutation problems. An interesting phenomenon that we prove is that for one formulation the problem can be solved adaptively, but for the other formulation no adaptive algorithm can be better than an optimal output-sensitive algorithm for the planar convex hull problem.
RESCALED PURE GREEDY ALGORITHM FOR CONVEX OPTIMIZATION
Petrova, Guergana
of these algorithms work only if the minimum of E is attained in the convex hull of D, since the approximant xm to the convex hull of D and has a rate of convergence O(m1-q). This algorithm is an appropriate modificationRESCALED PURE GREEDY ALGORITHM FOR CONVEX OPTIMIZATION ZHEMING GAO, GUERGANA PETROVA Abstract. We
A Convex Optimization Approach to pMRI Reconstruction
Zhang, Cishen
2013-01-01
In parallel magnetic resonance imaging (pMRI) reconstruction without using estimation of coil sensitivity functions, one group of algorithms reconstruct sensitivity encoded images of the coils first followed by the magnitude only image reconstruction, e.g. GRAPPA, and another group of algorithms jointly compute the image and sensitivity functions by regularized optimization which is a non-convex problem with local only solutions. For the magnitude only image reconstruction, this paper derives a reconstruction formulation, which is linear in the magnitude image, and an associated convex hull in the solution space of the formulated equation containing the magnitude of the image. As a result, the magnitude only image reconstruction for pMRI is formulated into a two-step convex optimization problem, which has a globally optimal solution. An algorithm based on split-bregman and nuclear norm regularized optimizations is proposed to implement the two-step convex optimization and its applications to phantom and in-vi...
10-725/36-725: Convex Optimization Spring 2015 Lecture 26: April 22nd
Tibshirani, Ryan
also implicitly mean doing it efficiently, i.e., in polynomial time. 26-1 #12;26-2 Lecture 26: April 2210-725/36-725: Convex Optimization Spring 2015 Lecture 26: April 22nd Lecturer: Ryan Tibshirani (to global optimality). 26.1 Non-convex problems Non-convex problems typically have higher variance
Lavaei, Javad
[3], [4], [5], [6], [7], dynamically decoupled systems [8], [9], weakly coupled systems [10 an optimal structured controller for a dynamical system subject to input disturbance and measurement noise sparsity pattern. The proposed technique is always exact for the classical H2 optimal control problem (i
Rapid Generation of Optimal Asteroid Powered Descent Trajectories Via Convex Optimization
NASA Technical Reports Server (NTRS)
Pinson, Robin; Lu, Ping
2015-01-01
This paper investigates a convex optimization based method that can rapidly generate the fuel optimal asteroid powered descent trajectory. The ultimate goal is to autonomously design the optimal powered descent trajectory on-board the spacecraft immediately prior to the descent burn. Compared to a planetary powered landing problem, the major difficulty is the complex gravity field near the surface of an asteroid that cannot be approximated by a constant gravity field. This paper uses relaxation techniques and a successive solution process that seeks the solution to the original nonlinear, nonconvex problem through the solutions to a sequence of convex optimal control problems.
Efficient Market Making via Convex Optimization, and a Connection to Online Learning
Chen, Yiling
12 Efficient Market Making via Convex Optimization, and a Connection to Online Learning JACOB of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded hull. By reducing the problem of automated market making to convex optimization, where many efficient
Marlin, Benjamin
/Distributed Optimization Convex Optimization for Big Data Asian Conference on Machine Learning Mark Schmidt November 2014/Distributed Optimization Context: Big Data and Big Models We are collecting data at unprecedented rates. Seen across many/Distributed Optimization Context: Big Data and Big Models We are collecting data at unprecedented rates. Seen across many
Intermediate gradient methods ^for smooth convex problems with inexact oracle
Glineur, François
2013/17 Intermediate gradient methods ^for smooth convex problems with inexact oracle Olivier DISCUSSION PAPER 2013/17 Intermediate gradient methods for smooth convex problems with inexact oracle Olivier ., . denotes the dual pairing. 1.1 Exact and Inexact Oracle Consider F1,1 L (Q), the class of convex functions
NEW LOWER BOUNDS FOR CONVEX HULL PROBLEMS IN ODD DIMENSIONS
Erickson, Jeff
. In 1970, Chand and Ka- pur 13] described a "gift-wrapping" algorithm that constructs convex hulls in arNEW LOWER BOUNDS FOR CONVEX HULL PROBLEMS IN ODD DIMENSIONS JEFF ERICKSONy Abstract. We show that in the worst case, (ndd=2e;1 +n logn) sidedness queries are required to determine whether the convex hull of n
New Lower Bounds for Convex Hull Problems in Odd Dimensions
Erickson, Jeff
described an algorithm that constructs the convex hull of n points in the plane in O(nlogn) time 15] describes an algorithm for constructing convex hulls in IRd in time O(nbd=2c + nlogn). Since an nNew Lower Bounds for Convex Hull Problems in Odd Dimensions Je Erickson Computer Science Division
Continuous-time distributed convex optimization on directed graphs
Gharesifard, Bahman
2012-01-01
This paper studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works for both undirected and directed scenarios, we show that the consensus-based dynamics that solves the continuous-time distributed optimization problem for undirected graphs fails to converge when transcribed to the directed setting. This study sets the basis for the design of an alternative distributed dynamics which we show is guaranteed to converge, on any strongly connected weight-balanced digraph, to the set of minimizers of a sum of convex differentiable functions with globally Lipschitz gradients. Our technical approach combines notions of invariance and cocoercivity with the positive definiteness properties of graph matrices to establish the results.
Phase retrieval using iterative Fourier transform and convex optimization algorithm
NASA Astrophysics Data System (ADS)
Zhang, Fen; Cheng, Hong; Zhang, Quanbing; Wei, Sui
2015-05-01
Phase is an inherent characteristic of any wave field. Statistics show that greater than 25% of the information is encoded in the amplitude term and 75% of the information is in the phase term. The technique of phase retrieval means acquire phase by computation using magnitude measurements and provides data information for holography display, 3D field reconstruction, X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Mathematically, solving phase retrieval problem is an inverse problem taking the physical and computation constraints. Some recent algorithms use the principle of compressive sensing, such as PhaseLift, PhaseCut and compressive phase retrieval etc. they formulate phase retrieval problems as one of finding the rank-one solution to a system of linear matrix equations and make the overall algorithm a convex program over n × n matrices. However, by "lifting" a vector problem to a matrix one, these methods lead to a much higher computational cost as a result. Furthermore, they only use intensity measurements but few physical constraints. In the paper, a new algorithm is proposed that combines above convex optimization methods with a well known iterative Fourier transform algorithm (IFTA). The IFTA iterates between the object domain and spectral domain to reinforce the physical information and reaches convergence quickly which has been proved in many applications such as compute-generated-hologram (CGH). Herein the output phase of the IFTA is treated as the initial guess of convex optimization methods, and then the reconstructed phase is numerically computed by using modified TFOCS. Simulation results show that the combined algorithm increases the likelihood of successful recovery as well as improves the precision of solution.
Kernel regression for travel time estimation via convex optimization
Kernel regression for travel time estimation via convex optimization Sébastien Blandin , Laurent El Ghaoui and Alexandre Bayen Abstract--We develop an algorithm aimed at estimating travel time on segments of a road network using a convex optimiza- tion framework. Sampled travel time from probe vehicles
First-order Methods for Convex Optimization with Inexact Oracle
Glineur, François
Examples of inexact oracles 4 Effect of inexact oracle on GM/FGM 5 Applications in Non-smooth Convex Examples of inexact oracles 4 Effect of inexact oracle on GM/FGM 5 Applications in Non-smooth Convex Optimization, two main FOM: 1 Gradient method (GM) 2 Fast gradient method (FGM) 6 #12;Gradient Method Very
Stochastic first order methods in smooth convex optimization
Glineur, FranÃ§ois
://www.uclouvain.be/core DISCUSSION PAPER #12;CORE DISCUSSION PAPER 2011/70 Stochastic first order methods in smooth convex by the author. #12;January 13, 2012 2 1 Introduction This paper is devoted to the development of efficient first2011/70 Stochastic first order methods in smooth convex optimization Olivier Devolder Center
Motion Planning with Sequential Convex Optimization and Convex Collision Checking
Patil, Sachin
3D-printed implants for intracavitary brachytherapy. Details, videos, and source code is freely trajectories, and (f) optimized layout for bounded curvature channels within 3D-printed vaginal implants-planning is necessary. Sampling-based motion planners [Kavraki et al., 1996; LaValle, 2006] are very effective and offer
Convex Hull Problems The construction of convex hulls is perhaps the oldest and beststudied problems
Erickson, Jeff
, 136, 142]. Over twenty years ago, Graham described an algorithm that constructs the convex hull of n] described an algorithm that constructs convex hulls in time O(nf), where f is the number of facets on which current convex hull algorithms perform quite badly, sometimes requiring exponential time (in d
Regularization Constants in LS-SVMs: a Fast Estimate via Convex Optimization
Regularization Constants in LS-SVMs: a Fast Estimate via Convex Optimization Kristiaan Pelckmans Support Vector Machines (LS-SVMs) for regression and classification is considered. The formulation of the LS-SVM training and regularization constant tuning problem (w.r.t. the validation performance
Byzantine Convex Consensus: An Optimal Algorithm Lewis Tseng1,3
Vaidya, Nitin
Byzantine Convex Consensus: An Optimal Algorithm Lewis Tseng1,3 , and Nitin Vaidya2,3 1 Department in the convex hull of the input vectors at the fault-free nodes [9, 13]. The d-dimensional vectors can to be a convex polytope in the d-dimensional space, such that the decided polytope is within the convex hull
GLOBAL OPTIMIZATION IN COMPUTER VISION: CONVEXITY, CUTS AND
Lunds Universitet
GLOBAL OPTIMIZATION IN COMPUTER VISION: CONVEXITY, CUTS AND APPROXIMATION ALGORITHMS CARL OLSSON in computer vision. Numerous prob- lems in this field as well as in image analysis and other branches. International Conference on Computer Vision (ICCV), Rio de Janeiro, Brazil, 2007. · C. Olsson, F. Kahl, R
FIR Filter Design via Spectral Factorization and Convex Optimization 1 FIR Filter Design via UCSB 10 24 97 FIR Filter Design via Spectral Factorization and Convex Optimization 2 Outline Convex optimization & interior-point methods FIR lters & magnitude specs Spectral factorization Examples lowpass lter
Low, Steven H.
SYSTEMS, JUNE 2014 (WITH PROOFS) 3 I. INTRODUCTION The optimal power flow (OPF) problem is fundamental Power Flow Part II: Exactness Steven H. Low Electrical Engineering, Computing+Mathematical Sciences recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural
Finding Locally Optimal, Collision-Free Trajectories with Sequential Convex Optimization
Abbeel, Pieter
Finding Locally Optimal, Collision-Free Trajectories with Sequential Convex Optimization John a novel approach for incorporating collision avoidance into trajectory optimization as a method of solving also compared to CHOMP, a leading approach for trajectory optimization. Our algorithm was faster than
A partially inexact bundle method for convex semi-infinite minmax problems
NASA Astrophysics Data System (ADS)
Fuduli, Antonio; Gaudioso, Manlio; Giallombardo, Giovanni; Miglionico, Giovanna
2015-04-01
We present a bundle method for solving convex semi-infinite minmax problems which allows inexact solution of the inner maximization. The method is of the partially inexact oracle type, and it is aimed at reducing the occurrence of null steps and at improving bundle handling with respect to existing methods. Termination of the algorithm is proved at a point satisfying an approximate optimality criterion, and the results of some numerical experiments are also reported.
Stochastic Convex Optimization with Multiple Objectives
Jin, Rong
stochastic multiple objective optimization is to linearly combine multiple objectives with a fixed weight r Rn denote random returns of the n risky assets, and w W {w Rn + : n i wi = 1} denote the distribution of an investor's wealth over all assets. The return for an investment distribution is defined as w
A Characterization Theorem and an Algorithm for a Convex Hull Problem Bahman Kalantari
Goldman, William
A Characterization Theorem and an Algorithm for a Convex Hull Problem Bahman Kalantari Extended Abstract. Given a set S = {v1, . . . , vn} Rm and a point p Rm , testing if p conv(S), the convex hull(p, p ) d(p, p) d(p, p ). (3) Not only this approximation is useful for the convex hull problem
Solving infinite-dimensional optimization problems by polynomial approximation
Glineur, François
2010/29 Solving infinite-dimensional optimization problems by polynomial approximation Olivier DISCUSSION PAPER 2010/29 Solving infinite-dimensional optimization problems by polynomial approximation of convex infinite-dimensional optimization problems using a numerical approximation method that does
NASA Astrophysics Data System (ADS)
Cevher, Volkan; Becker, Stephen; Schmidt, Mark
2014-09-01
This article reviews recent advances in convex optimization algorithms for Big Data, which aim to reduce the computational, storage, and communications bottlenecks. We provide an overview of this emerging field, describe contemporary approximation techniques like first-order methods and randomization for scalability, and survey the important role of parallel and distributed computation. The new Big Data algorithms are based on surprisingly simple principles and attain staggering accelerations even on classical problems.
Optimal Output-Sensitive Convex Hull Algorithms in Two and Three Dimensions
Danner, Andrew
Optimal Output-Sensitive Convex Hull Algorithms in Two and Three Dimensions Timothy M. Chan present simple output-sensitive algorithms that construct the convex hull of a set of n points in two the convex hull in O(nh) time. This bound was later improved to O(nlogh) by an algorithm due to Kirkpatrick
Optimal OutputSensitive Convex Hull Algorithms in Two and Three Dimensions
Chan, Timothy M.
Optimal OutputÂSensitive Convex Hull Algorithms in Two and Three Dimensions Timothy M. Chan \\Lambda present simple outputÂsensitive algorithms that construct the convex hull of a set of n points in two, we point out a simple outputÂsensitive convex hull algorithm in E 2 and its extension in E 3 , both
Studies integrating geometry, probability, and optimization under convexity
Nogueira, Alexandre Belloni
2006-01-01
Convexity has played a major role in a variety of fields over the past decades. Nevertheless, the convexity assumption continues to reveal new theoretical paradigms and applications. This dissertation explores convexity ...
NEW LOWER BOUNDS FOR CONVEX HULL PROBLEMS IN ODD DIMENSIONS \\Lambda
Erickson, Jeff
, 44, 47, 48]. Over twenty years ago, Graham described an algorithm that constructs the convex hullÂwrapping'' algorithm that constructs convex hulls in arÂ bitrary dimensions in time O(nf ); see also [47]. SeidelNEW LOWER BOUNDS FOR CONVEX HULL PROBLEMS IN ODD DIMENSIONS \\Lambda JEFF ERICKSON y Abstract. We
New Lower Bounds for Convex Hull Problems in Odd Dimensions \\Lambda
Erickson, Jeff
an algorithm that constructs the convex hull of n points in the plane in O(n log n) time [15]. The same runningÂ sions [10, 8]. Chazelle [7] describes an algorithm for constructing convex hulls in IR d in time O(n bdNew Lower Bounds for Convex Hull Problems in Odd Dimensions \\Lambda Jeff Erickson Computer Science
An Inner Convex Approximation Algorithm for BMI Optimization and Applications in Control
Dinh, Quoc Tran; Diehl, Moritz
2012-01-01
In this work, we propose a new local optimization method to solve a class of nonconvex semidefinite programming (SDP) problems. The basic idea is to approximate the feasible set of the nonconvex SDP problem by inner positive semidefinite convex approximations via a parameterization technique. This leads to an iterative procedure to search a local optimum of the nonconvex problem. The convergence of the algorithm is analyzed under mild assumptions. Applications in static output feedback control are benchmarked and numerical tests are implemented based on the data from the COMPLeib library.
Hybrid Random/Deterministic Parallel Algorithms for Convex and Nonconvex Big Data Optimization
NASA Astrophysics Data System (ADS)
Daneshmand, Amir; Facchinei, Francisco; Kungurtsev, Vyacheslav; Scutari, Gesualdo
2015-08-01
We propose a decomposition framework for the parallel optimization of the sum of a differentiable {(possibly nonconvex)} function and a nonsmooth (possibly nonseparable), convex one. The latter term is usually employed to enforce structure in the solution, typically sparsity. The main contribution of this work is a novel \\emph{parallel, hybrid random/deterministic} decomposition scheme wherein, at each iteration, a subset of (block) variables is updated at the same time by minimizing local convex approximations of the original nonconvex function. To tackle with huge-scale problems, the (block) variables to be updated are chosen according to a \\emph{mixed random and deterministic} procedure, which captures the advantages of both pure deterministic and random update-based schemes. Almost sure convergence of the proposed scheme is established. Numerical results show that on huge-scale problems the proposed hybrid random/deterministic algorithm outperforms both random and deterministic schemes.
Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process
Yin, Chuancun; Yuen, Kam Chuen; Shen, Ying
2015-01-01
We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy. PMID:26351655
Sparse representations and convex optimization as tools for LOFAR radio interferometric imaging
NASA Astrophysics Data System (ADS)
Girard, J. N.; Garsden, H.; Starck, J. L.; Corbel, S.; Woiselle, A.; Tasse, C.; McKean, J. P.; Bobin, J.
2015-08-01
Compressed sensing theory is slowly making its way to solve more and more astronomical inverse problems. We address here the application of sparse representations, convex optimization and proximal theory to radio interferometric imaging. First, we expose the theory behind interferometric imaging, sparse representations and convex optimization, and second, we illustrate their application with numerical tests with SASIR, an implementation of the FISTA, a Forward-Backward splitting algorithm hosted in a LOFAR imager. Various tests have been conducted in Garsden et al., 2015. The main results are: i) an improved angular resolution (super resolution of a factor ? 2) with point sources as compared to CLEAN on the same data, ii) correct photometry measurements on a field of point sources at high dynamic range and iii) the imaging of extended sources with improved fidelity. SASIR provides better reconstructions (five time less residuals) of the extended emission as compared to CLEAN. With the advent of large radiotelescopes, there is scope for improving classical imaging methods with convex optimization methods combined with sparse representations.
Erickson, Jeff
, 136, 142]. Over twenty years ago, Graham described an algorithm that constructs the convex hull of n that constructs convex hulls in time O(nf), where f is the number of facets in the output. An algorithm of Chan, 12] describe families of polytopes on which current convex hull algorithms perform quite badly
The minimum-error discrimination via Helstrom family of ensembles and Convex Optimization
M. A. Jafarizadeh; Y. Mazhari; M. Aali
2009-10-28
Using the convex optimization method and Helstrom family of ensembles introduced in Ref. [1], we have discussed optimal ambiguous discrimination in qubit systems. We have analyzed the problem of the optimal discrimination of N known quantum states and have obtained maximum success probability and optimal measurement for N known quantum states with equiprobable prior probabilities and equidistant from center of the Bloch ball, not all of which are on the one half of the Bloch ball and all of the conjugate states are pure. An exact solution has also been given for arbitrary three known quantum states. The given examples which use our method include: 1. Diagonal N mixed states; 2. N equiprobable states and equidistant from center of the Bloch ball which their corresponding Bloch vectors are inclined at the equal angle from z axis; 3. Three mirror-symmetric states; 4. States that have been prepared with equal prior probabilities on vertices of a Platonic solid. Keywords: minimum-error discrimination, success probability, measurement, POVM elements, Helstrom family of ensembles, convex optimization, conjugate states PACS Nos: 03.67.Hk, 03.65.Ta
Approximate D-optimal designs of experiments on the convex hull of a finite set
Trnovska, Maria
Approximate D-optimal designs of experiments on the convex hull of a finite set of information-optimality covers many special design settings, e.g. the D-optimal experimental design for re- gression models of standard D-optimality. Moreover, we show that DH-optimal designs can be numerically computed using
BROADBAND SENSOR LOCATION SELECTION USING CONVEX OPTIMIZATION IN VERY LARGE SCALE ARRAYS
Balan, Radu V.
BROADBAND SENSOR LOCATION SELECTION USING CONVEX OPTIMIZATION IN VERY LARGE SCALE ARRAYS Yenming M pattern design, sensor location selection, very large scale arrays, convex op- timization, simulated annealing 1. INTRODUCTION Consider a large scale sensor array having N sensors that monitors a surveillance
Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization
Toint, Philippe
Evaluation complexity of adaptive cubic regularization methods for convex unconstrained complexity of adaptive cubic regularization methods for convex unconstrained optimization C. Cartis , N. I. M.gould@sftc.ac.uk Namur Center for Complex Systems (NAXYS), FUNDP-University of Namur, 61, rue de Bruxelles, B-5000 Namur
A Localization Method for Multistatic SAR Based on Convex Optimization.
Zhong, Xuqi; Wu, Junjie; Yang, Jianyu; Sun, Zhichao; Huang, Yuling; Li, Zhongyu
2015-01-01
In traditional localization methods for Synthetic Aperture Radar (SAR), the bistatic range sum (BRS) estimation and Doppler centroid estimation (DCE) are needed for the calculation of target localization. However, the DCE error greatly influences the localization accuracy. In this paper, a localization method for multistatic SAR based on convex optimization without DCE is investigated and the influence of BRS estimation error on localization accuracy is analysed. Firstly, by using the information of each transmitter and receiver (T/R) pair and the target in SAR image, the model functions of T/R pairs are constructed. Each model function's maximum is on the circumference of the ellipse which is the iso-range for its model function's T/R pair. Secondly, the target function whose maximum is located at the position of the target is obtained by adding all model functions. Thirdly, the target function is optimized based on gradient descent method to obtain the position of the target. During the iteration process, principal component analysis is implemented to guarantee the accuracy of the method and improve the computational efficiency. The proposed method only utilizes BRSs of a target in several focused images from multistatic SAR. Therefore, compared with traditional localization methods for SAR, the proposed method greatly improves the localization accuracy. The effectivity of the localization approach is validated by simulation experiment. PMID:26566031
A Localization Method for Multistatic SAR Based on Convex Optimization
2015-01-01
In traditional localization methods for Synthetic Aperture Radar (SAR), the bistatic range sum (BRS) estimation and Doppler centroid estimation (DCE) are needed for the calculation of target localization. However, the DCE error greatly influences the localization accuracy. In this paper, a localization method for multistatic SAR based on convex optimization without DCE is investigated and the influence of BRS estimation error on localization accuracy is analysed. Firstly, by using the information of each transmitter and receiver (T/R) pair and the target in SAR image, the model functions of T/R pairs are constructed. Each model function’s maximum is on the circumference of the ellipse which is the iso-range for its model function’s T/R pair. Secondly, the target function whose maximum is located at the position of the target is obtained by adding all model functions. Thirdly, the target function is optimized based on gradient descent method to obtain the position of the target. During the iteration process, principal component analysis is implemented to guarantee the accuracy of the method and improve the computational efficiency. The proposed method only utilizes BRSs of a target in several focused images from multistatic SAR. Therefore, compared with traditional localization methods for SAR, the proposed method greatly improves the localization accuracy. The effectivity of the localization approach is validated by simulation experiment. PMID:26566031
NP-hardness of Deciding Convexity of Quartic Polynomials and Related Problems
Suresh, Subra
NP-hardness of Deciding Convexity of Quartic Polynomials and Related Problems Amir Ali Ahmadi, Alex of polynomials of even degree four or higher is strongly NP-hard. By contrast, we show that quasiconvexity in this paper (Theorem 2.1 in Section 2.3) is to show that deciding convexity of polynomials is strongly NP-hard
The optimal path-matching problem
Cunningham, W.H.; Geelen, J.F.
1996-12-31
We describe a common generalization of the weighted matching problem and the weighted matroid intersection problem. In this context we present results implying the polynomial-time solvability of the two problems. We also use our results to give the first strongly polynomial separation algorithm for the convex hull of matchable sets of a graph, and the first polynomial-time algorithm to compute the rank of a certain matrix of indeterminates. Our algorithmic results are based on polyhedral characterizations, and on the equivalence of separation and optimization.
Discrete convexity : retractions, morphisms and the partition problem
Duchet, Pierre
a pour nombre de Helly h , pour nombre de Radon p 2 et a un k Ã¨me nombre de partition (gÃ©odÃ©sique) au is geodetically convex if it contains the vertices of any shortest path joining two of its elements). For instance) a finite connected graph whose (geodetic) convexity has Helly number h, Radon number p 2 and a k
Implementation of a Point Algorithm for Real-Time Convex Optimization
NASA Technical Reports Server (NTRS)
Acikmese, Behcet; Motaghedi, Shui; Carson, John
2007-01-01
The primal-dual interior-point algorithm implemented in G-OPT is a relatively new and efficient way of solving convex optimization problems. Given a prescribed level of accuracy, the convergence to the optimal solution is guaranteed in a predetermined, finite number of iterations. G-OPT Version 1.0 is a flight software implementation written in C. Onboard application of the software enables autonomous, real-time guidance and control that explicitly incorporates mission constraints such as control authority (e.g. maximum thrust limits), hazard avoidance, and fuel limitations. This software can be used in planetary landing missions (Mars pinpoint landing and lunar landing), as well as in proximity operations around small celestial bodies (moons, asteroids, and comets). It also can be used in any spacecraft mission for thrust allocation in six-degrees-of-freedom control.
Equivalence of Convex Problem Geometry and Computational Complexity in the Separation Oracle Model
Vera Andreo, Jorge R.
Consider the supposedly simple problem of computing a point in a convex set that is conveyed by a separation oracle with no further information (e.g., no domain ball containing or intersecting the set, etc.). The authors' ...
libCreme: An optimization library for evaluating convex-roof entanglement measures
Beat Röthlisberger; Jörg Lehmann; Daniel Loss
2011-07-22
We present the software library libCreme which we have previously used to successfully calculate convex-roof entanglement measures of mixed quantum states appearing in realistic physical systems. Evaluating the amount of entanglement in such states is in general a non-trivial task requiring to solve a highly non-linear complex optimization problem. The algorithms provided here are able to achieve to do this for a large and important class of entanglement measures. The library is mostly written in the Matlab programming language, but is fully compatible to the free and open-source Octave platform. Some inefficient subroutines are written in C/C++ for better performance. This manuscript discusses the most important theoretical concepts and workings of the algorithms, focussing on the actual implementation and usage within the library. Detailed examples in the end should make it easy for the user to apply libCreme to specific problems.
An example of non-convex minimization and an application to Newton's problem of the
Peletier, Mark
.1 Newton's problem The problem of the body of minimal resistance was introduced by Sir Isaac NewtonAn example of non-convex minimization and an application to Newton's problem of the body of least is the problem of the body of least resistance as formulated by Newton (where f(p) = 1=(1+ jpj 2 ) and is a ball
Optimal In-Place and Cache-Oblivious Algorithms for 3-d Convex Hulls and 2-d Segment Intersection
Chan, Timothy M.
Optimal In-Place and Cache-Oblivious Algorithms for 3-d Convex Hulls and 2-d Segment Intersection-place algorithm for the basic 3-d convex hull prob- lem (and, in particular, for 2-d Voronoi diagrams: In-place algorithms, Convex hulls, Voronoi diagrams, Segment intersection, Cache- oblivious
Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions
Agarwal, Alekh
We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation [bar through "X" symbol] of the sum ...
Asynchronous Convex Consensus in the Presence of Crash Faults Lewis Tseng1
Vaidya, Nitin
within the convex hull of the inputs at the fault-free processes. We explore the convex consensus problem algorithm with optimal fault tolerance that reaches consensus on an optimal output polytope. Convex, and the processes reach consensus on a d-dimensional vector within the convex hull of the inputs at fault
Scalable analysis of nonlinear systems using convex optimization
NASA Astrophysics Data System (ADS)
Papachristodoulou, Antonis
In this thesis, we investigate how convex optimization can be used to analyze different classes of nonlinear systems at various scales algorithmically. The methodology is based on the construction of appropriate Lyapunov-type certificates using sum of squares techniques. After a brief introduction on the mathematical tools that we will be using, we turn our attention to robust stability and performance analysis of systems described by Ordinary Differential Equations. A general framework for constrained systems analysis is developed, under which stability of systems with polynomial, non-polynomial vector fields and switching systems, as well estimating the region of attraction and the L2 gain can be treated in a unified manner. We apply our results to examples from biology and aerospace. We then consider systems described by Functional Differential Equations (FDEs), i.e., time-delay systems. Their main characteristic is that they are infinite dimensional, which complicates their analysis. We first show how the complete Lyapunov-Krasovskii functional can be constructed algorithmically for linear time-delay systems. Then, we concentrate on delay-independent and delay-dependent stability analysis of nonlinear FDEs using sum of squares techniques. An example from ecology is given. The scalable stability analysis of congestion control algorithms for the Internet is investigated next. The models we use result in an arbitrary interconnection of FDE subsystems, for which we require that stability holds for arbitrary delays, network topologies and link capacities. Through a constructive proof, we develop a Lyapunov functional for FAST---a recently developed network congestion control scheme---so that the Lyapunov stability properties scale with the system size. We also show how other network congestion control schemes can be analyzed in the same way. Finally, we concentrate on systems described by Partial Differential Equations. We show that axially constant perturbations of the Navier-Stokes equations for Hagen-Poiseuille flow are globally stable, even though the background noise is amplified as R3 where R is the Reynolds number, giving a 'robust yet fragile' interpretation. We also propose a sum of squares methodology for the analysis of systems described by parabolic PDEs. We conclude this work with an account for future research.
The minimum-error discrimination via Helstrom family of ensembles and Convex Optimization
Jafarizadeh, M A; Aali, M
2009-01-01
Using the convex optimization method and Helstrom family of ensembles introduced in Ref. [1], we have discussed optimal ambiguous discrimination in qubit systems. We have analyzed the problem of the optimal discrimination of N known quantum states and have obtained maximum success probability and optimal measurement for N known quantum states with equiprobable prior probabilities and equidistant from center of the Bloch ball, not all of which are on the one half of the Bloch ball and all of the conjugate states are pure. An exact solution has also been given for arbitrary three known quantum states. The given examples which use our method include: 1. Diagonal N mixed states; 2. N equiprobable states and equidistant from center of the Bloch ball which their corresponding Bloch vectors are inclined at the equal angle from z axis; 3. Three mirror-symmetric states; 4. States that have been prepared with equal prior probabilities on vertices of a Platonic solid. Keywords: minimum-error discrimination, success prob...
Convex optimization of coincidence time resolution for a high-resolution PET system.
Reynolds, Paul D; Olcott, Peter D; Pratx, Guillem; Lau, Frances W Y; Levin, Craig S
2011-02-01
We are developing a dual panel breast-dedicated positron emission tomography (PET) system using LSO scintillators coupled to position sensitive avalanche photodiodes (PSAPD). The charge output is amplified and read using NOVA RENA-3 ASICs. This paper shows that the coincidence timing resolution of the RENA-3 ASIC can be improved using certain list-mode calibrations. We treat the calibration problem as a convex optimization problem and use the RENA-3's analog-based timing system to correct the measured data for time dispersion effects from correlated noise, PSAPD signal delays and varying signal amplitudes. The direct solution to the optimization problem involves a matrix inversion that grows order (n(3)) with the number of parameters. An iterative method using single-coordinate descent to approximate the inversion grows order (n). The inversion does not need to run to convergence, since any gains at high iteration number will be low compared to noise amplification. The system calibration method is demonstrated with measured pulser data as well as with two LSO-PSAPD detectors in electronic coincidence. After applying the algorithm, the 511 keV photopeak paired coincidence time resolution from the LSO-PSAPD detectors under study improved by 57%, from the raw value of 16.3 ±0.07 ns full-width at half-maximum (FWHM) to 6.92 ±0.02 ns FWHM ( 11.52 ±0.05 ns to 4.89 ±0.02 ns for unpaired photons). PMID:20876008
Exact Convex Relaxation of Optimal Power Flow in Radial Networks
Gan, LW; Li, N; Topcu, U; Low, SH
2015-01-01
The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. It is nonconvex. We prove that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial power networks. The condition can be checked a priori, and holds for the IEEE 13, 34, 37, 123-bus networks and two real-world networks.
The role of convexity for solving some shortest path problems in plane without triangulation
NASA Astrophysics Data System (ADS)
An, Phan Thanh; Hai, Nguyen Ngoc; Hoai, Tran Van
2013-09-01
Solving shortest path problems inside simple polygons is a very classical problem in motion planning. To date, it has usually relied on triangulation of the polygons. The question: "Can one devise a simple O(n) time algorithm for computing the shortest path between two points in a simple polygon (with n vertices), without resorting to a (complicated) linear-time triangulation algorithm?" raised by J. S. B. Mitchell in Handbook of Computational Geometry (J. Sack and J. Urrutia, eds., Elsevier Science B.V., 2000), is still open. The aim of this paper is to show that convexity contributes to the design of efficient algorithms for solving some versions of shortest path problems (namely, computing the convex hull of a finite set of points and convex rope on rays in 2D, computing approximate shortest path between two points inside a simple polygon) without triangulation on the entire polygons. New algorithms are implemented in C and numerical examples are presented.
libCreme: An optimization library for evaluating convex-roof entanglement measures
NASA Astrophysics Data System (ADS)
Röthlisberger, Beat; Lehmann, Jörg; Loss, Daniel
2012-01-01
We present the software library libCreme which we have previously used to successfully calculate convex-roof entanglement measures of mixed quantum states appearing in realistic physical systems. Evaluating the amount of entanglement in such states is in general a non-trivial task requiring to solve a highly non-linear complex optimization problem. The algorithms provided here are able to achieve to do this for a large and important class of entanglement measures. The library is mostly written in the MATLAB programming language, but is fully compatible to the free and open-source OCTAVE platform. Some inefficient subroutines are written in C/C++ for better performance. This manuscript discusses the most important theoretical concepts and workings of the algorithms, focusing on the actual implementation and usage within the library. Detailed examples in the end should make it easy for the user to apply libCreme to specific problems. Program summaryProgram title:libCreme Catalogue identifier: AEKD_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKD_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL version 3 No. of lines in distributed program, including test data, etc.: 4323 No. of bytes in distributed program, including test data, etc.: 70 542 Distribution format: tar.gz Programming language: Matlab/Octave and C/C++ Computer: All systems running Matlab or Octave Operating system: All systems running Matlab or Octave Classification: 4.9, 4.15 Nature of problem: Evaluate convex-roof entanglement measures. This involves solving a non-linear (unitary) optimization problem. Solution method: Two algorithms are provided: A conjugate-gradient method using a differential-geometric approach and a quasi-Newton method together with a mapping to Euclidean space. Running time: Typically seconds to minutes for a density matrix of a few low-dimensional systems and a decent implementation of the pure-state entanglement measure.
Information-theoretic lower bounds on the oracle complexity of convex optimization
Ravikumar, Pradeep
of Statistics UC Berkeley wainwrig@eecs.berkeley.edu Abstract Despite a large literature on upper bounds Department of Statistics UC Berkeley bartlett@cs.berkeley.edu Pradeep Ravikumar Department of Computer of these prob- lems. Given the extensive use of convex optimization in machine learning and statistics, gaining
A Convex Optimization Approach to Modeling Consumer Heterogeneity in Conjoint Estimation
Pontil, Massimiliano
, Econometric Models, Estimation and Other Statistical Techniques, Hierarchical Bayes Analysis, Marketing-based conjoint estimation using convex optimization and statistical machine learning. We compare our approach with hierarchical Bayes (HB) both theoretically and empirically. Both our methods and HB shrink individual
Limit shape of optimal convex lattice polygons . . . 1 LIMIT SHAPE OF
Stojakovic, Milos
and explicitly find the limit shape of the sequence of these optimal convex lattice polygons as the number() Ip , Cp y () Ip ) , 0 ) , Cp y () = 2 ( - 1 3 (p + 1)-3/p + k=0 ( -3 p - 1 k ) pk pk + 2 ) , Ip = 1 0 ( p 1 - lp)2 dl. Some
Design on Non-Convex Regions: Optimal Experiments for Spatial Process Prediction
Brennand, Tracy
Pratola B.Sc., 2005. Brock University a project submitted in partial fulfillment of the requirements: Matthew Timothy Pratola Degree: Master of Science Title of project: Design on Non-Convex Regions: Optimal from the Department of Math- ematics and Computer Science at Duquesne University for providing
GUIDED SEARCH CONSENSUS: LARGE SCALE POINT CLOUD REGISTRATION BY CONVEX OPTIMIZATION
Instituto de Sistemas e Robotica
GUIDED SEARCH CONSENSUS: LARGE SCALE POINT CLOUD REGISTRATION BY CONVEX OPTIMIZATION Manuel Marques the kind of patterns that makeup the large artistic tile panel on the background. These panels are pieces. Typical application: Searching for repetitive patterns on a tile panel. palaces and historic buildings
10-725: Convex Optimization Fall 2013 Lecture 9: Newton Method
Tibshirani, Ryan
's method, the formal Newton method began to evolve from Isaac Newton (1669) for finding roots10-725: Convex Optimization Fall 2013 Lecture 9: Newton Method Lecturer: Barnabas Poczos.1 Motivation Newton method is originally developed for finding a root of a function. It is also known as Newton
Optimal structural design via optimality criteria as a nonsmooth mechanics problem
NASA Astrophysics Data System (ADS)
Tzaferopoulos, M. Ap.; Stravroulakis, G. E.
1995-06-01
In the theory of plastic structural design via optimality criteria (due to W. Prager), the optimal design problem is transformed to a nonlinear elastic structural analysis problem with appropriate stress-strain laws, which generally include complete vertical branches. In this context, the concept of structural universe (in the sense of G. Rozvany) permits the treatment of complicated optimal layout problems. Recent progress in the field of nonsmooth mechanics makes the solution of structural analysis problems with this kind of 'complete' law possible. Elements from the two fields are combined in this paper for the solution of optimal design and layout problems for structures. The optimal layout of plane trusses with various specific cost functions is studied here as a representative problem. The use of convex, continuous and piecewise linear specific cost functions for the structural members leads to problems of linear variational inequalities or equivalently piecewise linear, convex but nonsmooth optimization problems, which are solved by means of an iterative algorithm based on sequential linear programming techniques. Numerical examples illustrate the theory and its applicability to practical engineering structures. Following a parametric investigation of an optimal bridge design, certain aspects of the optimal truss layout problem are discussed, which can be extended to other types of structural systems as well.
Wang, Li; Gao, Yaozong; Shi, Feng; Liao, Shu; Li, Gang; Chen, Ken Chung; Shen, Steve G. F.; Yan, Jin; Lee, Philip K. M.; Chow, Ben; Liu, Nancy X.; Xia, James J.; Department of Surgery , Weill Medical College, Cornell University, New York, New York 10065; Department of Oral and Craniomaxillofacial Surgery and Science, Shanghai Ninth People's Hospital, Shanghai Jiao Tong University College of Medicine, Shanghai, China 200011 ; Shen, Dinggang
2014-04-15
Purpose: Cone-beam computed tomography (CBCT) is an increasingly utilized imaging modality for the diagnosis and treatment planning of the patients with craniomaxillofacial (CMF) deformities. Accurate segmentation of CBCT image is an essential step to generate three-dimensional (3D) models for the diagnosis and treatment planning of the patients with CMF deformities. However, due to the poor image quality, including very low signal-to-noise ratio and the widespread image artifacts such as noise, beam hardening, and inhomogeneity, it is challenging to segment the CBCT images. In this paper, the authors present a new automatic segmentation method to address these problems. Methods: To segment CBCT images, the authors propose a new method for fully automated CBCT segmentation by using patch-based sparse representation to (1) segment bony structures from the soft tissues and (2) further separate the mandible from the maxilla. Specifically, a region-specific registration strategy is first proposed to warp all the atlases to the current testing subject and then a sparse-based label propagation strategy is employed to estimate a patient-specific atlas from all aligned atlases. Finally, the patient-specific atlas is integrated into amaximum a posteriori probability-based convex segmentation framework for accurate segmentation. Results: The proposed method has been evaluated on a dataset with 15 CBCT images. The effectiveness of the proposed region-specific registration strategy and patient-specific atlas has been validated by comparing with the traditional registration strategy and population-based atlas. The experimental results show that the proposed method achieves the best segmentation accuracy by comparison with other state-of-the-art segmentation methods. Conclusions: The authors have proposed a new CBCT segmentation method by using patch-based sparse representation and convex optimization, which can achieve considerably accurate segmentation results in CBCT segmentation based on 15 patients.
NASA Astrophysics Data System (ADS)
Panicker, Rahul Alex
Multimode fibers (MMF) are widely deployed in local-, campus-, and storage-area-networks. Achievable data rates and transmission distances are, however, limited by the phenomenon of modal dispersion. We propose a system to compensate for modal dispersion using adaptive optics. This leads to a 10- to 100-fold improvement in performance over current standards. We propose a provably optimal technique for minimizing inter-symbol interference (ISI) in MMF systems using adaptive optics via convex optimization. We use a spatial light modulator (SLM) to shape the spatial profile of light launched into an MMF. We derive an expression for the system impulse response in terms of the SLM reflectance and the field patterns of the MMF principal modes. Finding optimal SLM settings to minimize ISI, subject to physical constraints, is posed as an optimization problem. We observe that our problem can be cast as a second-order cone program, which is a convex optimization problem. Its global solution can, therefore, be found with minimal computational complexity. Simulations show that this technique opens up an eye pattern originally closed due to ISI. We then propose fast, low-complexity adaptive algorithms for optimizing the SLM settings. We show that some of these converge to the global optimum in the absence of noise. We also propose modified versions of these algorithms to improve resilience to noise and speed of convergence. Next, we experimentally compare the proposed adaptive algorithms in 50-mum graded-index (GRIN) MMFs using a liquid-crystal SLM. We show that continuous-phase sequential coordinate ascent (CPSCA) gives better bit-error-ratio performance than 2- or 4-phase sequential coordinate ascent, in concordance with simulations. We evaluate the bandwidth characteristics of CPSCA, and show that a single SLM is able to simultaneously compensate over up to 9 wavelength-division-multiplexed (WDM) 10-Gb/s channels, spaced by 50 GHz, over a total bandwidth of 450 GHz. We also show that CPSCA is able to compensate for modal dispersion over up to 2.2 km, even in the presence of mid-span connector offsets up to 4 mum (simulated in experiment by offset splices). A known non-adaptive launching technique using a fusion-spliced single-mode-to-multimode patchcord is shown to fail under these conditions. Finally, we demonstrate 10 x 10 Gb/s dense WDM transmission over 2.2 km of 50-mum GRIN MMF. We combine transmitter-based adaptive optics and receiver-based single-mode filtering, and control the launched field pattern for ten 10-Gb/s non-return-to-zero channels, wavelength-division multiplexed on a 200-GHz grid in the C band. We achieve error-free transmission through 2.2 km of 50-mum GRIN MMF for launch offsets up to 10 mum and for worst-case launched polarization. We employ a ten-channel transceiver based on parallel integration of electronics and photonics.
Partial Stabilizability and Hidden Convexity of an Indefinite LQ Problem
Moore, John Barratt
. There is no prior assumption of complete stabilizability. A generalized algebraic Riccati equation is introduced-stabilizability, generalized al- gebraic Riccati equation, linear matrix inequality, semi-definite pro- gramming to the classical Riccati equation [13], much research has been devoted to the optimization of more general
Class and Home Problems: Optimization Problems
ERIC Educational Resources Information Center
Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard
2011-01-01
Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…
SLOPE—ADAPTIVE VARIABLE SELECTION VIA CONVEX OPTIMIZATION
Bogdan, Ma?gorzata; van den Berg, Ewout; Sabatti, Chiara; Su, Weijie; Candès, Emmanuel J.
2015-01-01
We introduce a new estimator for the vector of coefficients ? in the linear model y = X? + z, where X has dimensions n × p with p possibly larger than n. SLOPE, short for Sorted L-One Penalized Estimation, is the solution to minb??p12?y?Xb??22+?1|b|(1)+?2|b|(2)+?+?p|b|(p),where ?1 ? ?2 ? … ? ?p ? 0 and |b|(1)?|b|(2)???|b|(p) are the decreasing absolute values of the entries of b. This is a convex program and we demonstrate a solution algorithm whose computational complexity is roughly comparable to that of classical ?1 procedures such as the Lasso. Here, the regularizer is a sorted ?1 norm, which penalizes the regression coefficients according to their rank: the higher the rank—that is, stronger the signal—the larger the penalty. This is similar to the Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289–300] procedure (BH) which compares more significant p-values with more stringent thresholds. One notable choice of the sequence {?i} is given by the BH critical values ?BH(i)=z(1?i?q/2p), where q ? (0, 1) and z(?) is the quantile of a standard normal distribution. SLOPE aims to provide finite sample guarantees on the selected model; of special interest is the false discovery rate (FDR), defined as the expected proportion of irrelevant regressors among all selected predictors. Under orthogonal designs, SLOPE with ?BH provably controls FDR at level q. Moreover, it also appears to have appreciable inferential properties under more general designs X while having substantial power, as demonstrated in a series of experiments running on both simulated and real data.
Chintala, Rohit
2012-10-19
Numerical methods of designing control systems are currently an active area of research. Convex optimization with linear matrix inequalities (LMIs) is one such method. Control objectives like minimizing the H_2, H_infinity ...
Advances in Convex Optimization: Theory, Algorithms, and Applications
processing, circuit design, . . . ISIT 02 Lausanne 7/3/02 9 #12;Recent history · (198497) interior new standard problem classes · generalized inequalities and semidefinite programming · interior ISIT 02 Lausanne 7/3/02 8 #12;What's new (since 1990 or so) · powerful primal-dual interior
Nonnegative Mixed-Norm Convex Optimization for Mitotic Cell Detection in Phase Contrast Microscopy
Hao, Tong; Gao, Zan; Su, Yuting; Yang, Zhaoxuan
2013-01-01
This paper proposes a nonnegative mix-norm convex optimization method for mitotic cell detection. First, we apply an imaging model-based microscopy image segmentation method that exploits phase contrast optics to extract mitotic candidates in the input images. Then, a convex objective function regularized by mix-norm with nonnegative constraint is proposed to induce sparsity and consistence for discriminative representation of deformable objects in a sparse representation scheme. At last, a Support Vector Machine classifier is utilized for mitotic cell modeling and detection. This method can overcome the difficulty in feature formulation for deformable objects and is independent of tracking or temporal inference model. The comparison experiments demonstrate that the proposed method can produce competing results with the state-of-the-art methods. PMID:24348733
A Weiszfeld-like algorithm for a Weber location problem constrained to a closed and convex set
Torres, Germán A
2012-01-01
The Weber problem consists of finding a point in $\\mathbbm{R}^n$ that minimizes the weighted sum of distances from $m$ points in $\\mathbbm{R}^n$ that are not collinear. An application that motivated this problem is the optimal location of facilities in the 2-dimensional case. A classical method to solve the Weber problem, proposed by Weiszfeld in 1937, is based on a fixed point iteration. In this work a Weber problem constrained to a closed and convex set is considered. A Weiszfeld-like algorithm, well defined even when an iterate is a vertex, is presented. The iteration function $Q$ that defines the proposed algorithm, is based mainly on an orthogonal projection over the feasible set, combined with the iteration function of the modified Weiszfeld algorithm presented by Vardi and Zhang in 2001. It can be proved that $x^*$ is a fixed point of the iteration function $Q$ if and only if $x^*$ is the solution of the constrained Weber problem. Besides that, under certain hypotheses, $x^*$ satisfies the KKT optimali...
Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems
NASA Technical Reports Server (NTRS)
Blackmore, Lars; Acikmese, Behcet; Carson, John M.,III
2012-01-01
In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.
Space-efficient algorithms for computing the convex hull of a simple polygonal line
Chan, Timothy M.
Space-efficient algorithms for computing the convex hull of a simple polygonal line in linear timeÂ¨onnimann et al. give optimal in-place algorithms for computing two-dimensional convex hulls. For this problem for stable partition. If the points inside the convex hull can be discarded, then there is a truly simple so
Rapid Generation of Optimal Asteroid Powered Descent Trajectories Via Convex Optimization
NASA Technical Reports Server (NTRS)
Pinson, Robin; Lu, Ping
2015-01-01
Mission proposals that land on asteroids are becoming popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site. The problem under investigation is how to design a fuel-optimal powered descent trajectory that can be quickly computed on-board the spacecraft, without interaction from ground control. An optimal trajectory designed immediately prior to the descent burn has many advantages. These advantages include the ability to use the actual vehicle starting state as the initial condition in the trajectory design and the ease of updating the landing target site if the original landing site is no longer viable. For long trajectories, the trajectory can be updated periodically by a redesign of the optimal trajectory based on current vehicle conditions to improve the guidance performance. One of the key drivers for being completely autonomous is the infrequent and delayed communication between ground control and the vehicle. Challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies and low thrust vehicles.
Anitescu, M.; Hart, G. D.; Mathematics and Computer Science; Univ. Pittsburg
2003-01-01
Time-stepping methods using impulse-velocity approaches are guaranteed to have a solution for any friction coefficient, but they may have nonconvex solution sets. We present an example of a configuration with a nonconvex solution set for any nonzero value of the friction coefficient. We construct an iterative algorithm that solves convex subproblems and that is guaranteed, for sufficiently small friction coefficients, to retrieve, at a linear convergence rate, the velocity solution of the nonconvex linear complementarity problem whenever the frictionless configuration can be disassembled. In addition, we show that one step of the iterative algorithm provides an excellent approximation to the velocity solution of the original, possibly nonconvex, problem if the product between the friction coefficient and the slip velocity is small.
Shape Optimization Problems over Classes of Convex Domains
Guasoni, Paolo
Principia Mathematica, at the early stages of Calculus of Variations. Newton's model was very simple: he resistance for a body moving in a fluid has a long history: it was first posed in 1685 by Newton in his
Formulating Cyber-Security as Convex Optimization Problems
Vigna, Giovanni
be found in trading, banking, power systems management, road traffic managements, healthcare, online order, submitting a paper to a conference through an online submission system, or printing a bank statement at an ATM machine. Cyber-missions typically require a large num- ber of computer services
Formulating Cyber-Security as Convex Optimization Problems
Hespanha, João Pedro
to a conference through an online submission system, or printing a bank statement at an ATM machine. Cyber. Cyber-missions are pervasive and can be found in trading, banking, power systems management, road traffic managements, healthcare, online shopping, business-to-business transactions, etc. The disruption
Optimization and geophysical inverse problems
Barhen, J.; Berryman, J.G.; Borcea, L.; Dennis, J.; de Groot-Hedlin, C.; Gilbert, F.; Gill, P.; Heinkenschloss, M.; Johnson, L.; McEvilly, T.; More, J.; Newman, G.; Oldenburg, D.; Parker, P.; Porto, B.; Sen, M.; Torczon, V.; Vasco, D.; Woodward, N.B.
2000-10-01
A fundamental part of geophysics is to make inferences about the interior of the earth on the basis of data collected at or near the surface of the earth. In almost all cases these measured data are only indirectly related to the properties of the earth that are of interest, so an inverse problem must be solved in order to obtain estimates of the physical properties within the earth. In February of 1999 the U.S. Department of Energy sponsored a workshop that was intended to examine the methods currently being used to solve geophysical inverse problems and to consider what new approaches should be explored in the future. The interdisciplinary area between inverse problems in geophysics and optimization methods in mathematics was specifically targeted as one where an interchange of ideas was likely to be fruitful. Thus about half of the participants were actively involved in solving geophysical inverse problems and about half were actively involved in research on general optimization methods. This report presents some of the topics that were explored at the workshop and the conclusions that were reached. In general, the objective of a geophysical inverse problem is to find an earth model, described by a set of physical parameters, that is consistent with the observational data. It is usually assumed that the forward problem, that of calculating simulated data for an earth model, is well enough understood so that reasonably accurate synthetic data can be generated for an arbitrary model. The inverse problem is then posed as an optimization problem, where the function to be optimized is variously called the objective function, misfit function, or fitness function. The objective function is typically some measure of the difference between observational data and synthetic data calculated for a trial model. However, because of incomplete and inaccurate data, the objective function often incorporates some additional form of regularization, such as a measure of smoothness or distance from a prior model. Various other constraints may also be imposed upon the process. Inverse problems are not restricted to geophysics, but can be found in a wide variety of disciplines where inferences must be made on the basis of indirect measurements. For instance, most imaging problems, whether in the field of medicine or non-destructive evaluation, require the solution of an inverse problem. In this report, however, the examples used for illustration are taken exclusively from the field of geophysics. The generalization of these examples to other disciplines should be straightforward, as all are based on standard second-order partial differential equations of physics. In fact, sometimes the non-geophysical inverse problems are significantly easier to treat (as in medical imaging) because the limitations on data collection, and in particular on multiple views, are not so severe as they generally are in geophysics. This report begins with an introduction to geophysical inverse problems by briefly describing four canonical problems that are typical of those commonly encountered in geophysics. Next the connection with optimization methods is made by presenting a general formulation of geophysical inverse problems. This leads into the main subject of this report, a discussion of methods for solving such problems with an emphasis upon newer approaches that have not yet become prominent in geophysics. A separate section is devoted to a subject that is not encountered in all optimization problems but is particularly important in geophysics, the need for a careful appraisal of the results in terms of their resolution and uncertainty. The impact on geophysical inverse problems of continuously improving computational resources is then discussed. The main results are then brought together in a final summary and conclusions section.
Interval-valued optimization problems involving (?, ?)-right upper-Dini-derivative functions.
Preda, Vasile
2014-01-01
We consider an interval-valued multiobjective problem. Some necessary and sufficient optimality conditions for weak efficient solutions are established under new generalized convexities with the tool-right upper-Dini-derivative, which is an extension of directional derivative. Also some duality results are proved for Wolfe and Mond-Weir duals. PMID:24982989
Interval-Valued Optimization Problems Involving (?, ?)-Right Upper-Dini-Derivative Functions
2014-01-01
We consider an interval-valued multiobjective problem. Some necessary and sufficient optimality conditions for weak efficient solutions are established under new generalized convexities with the tool-right upper-Dini-derivative, which is an extension of directional derivative. Also some duality results are proved for Wolfe and Mond-Weir duals. PMID:24982989
Convex hull based neuro-retinal optic cup ellipse optimization in glaucoma diagnosis.
Zhang, Zhuo; Liu, Jiang; Cherian, Neetu Sara; Sun, Ying; Lim, Joo Hwee; Wong, Wing Kee; Tan, Ngan Meng; Lu, Shijian; Li, Huiqi; Wong, Tien Ying
2009-01-01
Glaucoma is the second leading cause of blindness. Glaucoma can be diagnosed through measurement of neuro-retinal optic cup-to-disc ratio (CDR). Automatic calculation of optic cup boundary is challenging due to the interweavement of blood vessels with the surrounding tissues around the cup. A Convex Hull based Neuro-Retinal Optic Cup Ellipse Optimization algorithm improves the accuracy of the boundary estimation. The algorithm's effectiveness is demonstrated on 70 clinical patient's data set collected from Singapore Eye Research Institute. The root mean squared error of the new algorithm is 43% better than the ARGALI system which is the state-of-the-art. This further leads to a large clinical evaluation of the algorithm involving 15 thousand patients from Australia and Singapore. PMID:19963748
Linear-Convex Control and Duality R.T. Rockafellar
Goebel, Rafal
. For simplicity of presentation, but also with control engineering applications in mind, we specialize the keyLinear-Convex Control and Duality R.T. Rockafellar and Rafal Goebel April 2, 2007 Abstract An optimal control problem with linear dynamics and convex but not necessarily quadratic and possibly
NASA Astrophysics Data System (ADS)
Chen, Shibing; Wang, Xu-Jia
2016-01-01
In this paper we prove the strict c-convexity and the C 1, ? regularity for potential functions in optimal transportation under condition (A3w). These results were obtained by Caffarelli [1,3,4] for the cost c (x, y) =| x - y | 2, by Liu [11], Loeper [15], Trudinger and Wang [20] for costs satisfying the condition (A3). For costs satisfying the condition (A3w), the results have also been proved by Figalli, Kim, and McCann [6], assuming that the initial and target domains are uniformly c-convex, see also [21]; and by Guillen and Kitagawa [8], assuming the cost function satisfies A3w in larger domains. In this paper we prove the strict c-convexity and the C 1, ? regularity assuming either the support of source density is compactly contained in a larger domain where the cost function satisfies A3w, or the dimension 2 ? n ? 4.
Towards Optimal Techniques for Solving Global Optimization Problems
Kreinovich, Vladik
Towards Optimal Techniques for Solving Global Optimization Problems: Symmetry-Based Approach at El Paso, El Paso, TX 79968, USA vladik@utep.edu 1 Introduction 1.1 Global Optimization an Important of global optimization. Similar problems arise in data processing, when we have a model char- acterized
Towards Optimal Techniques for Solving Global Optimization Problems
Kreinovich, Vladik
Towards Optimal Techniques for Solving Global Optimization Problems: SymmetryBased Approach at El Paso, El Paso, TX 79968, USA vladik@utep.edu 1 Introduction 1.1 Global Optimization of global optimization. Similar problems arise in data processing, when we have a model char acterized
GLOBAL OPTIMALITY CONDITIONS FOR QUADRATIC OPTIMIZATION PROBLEMS WITH BINARY CONSTRAINTS
Beck, Amir
GLOBAL OPTIMALITY CONDITIONS FOR QUADRATIC OPTIMIZATION PROBLEMS WITH BINARY CONSTRAINTS AMIR BECK main result identifies a class of quadratic problems for which a given feasible point is global optimal. We also establish a necessary global optimality condition. These conditions are expressed in a simple
GLOBAL OPTIMIZATION FOR THE PHASE STABILITY PROBLEM
Neumaier, Arnold
GLOBAL OPTIMIZATION FOR THE PHASE STABILITY PROBLEM Conor M. McDonald and Christodoulos A. Floudas for this class of problems. The advantage of a global optimization approach is that if a nonnegative solution the efficiency of both global optimization algorithms in solving a variety of challenging problems. \\Lambda
A Characterization Theorem and An Algorithm for A Convex Hull Problem
Kalantari, Bahman
2012-01-01
Given a set $S= \\{v_1, ..., v_n\\} \\subset \\mathbb{R} ^m$ and a point $p \\in \\mathbb{R} ^m$, we wish to test if $p \\in {\\rm Conv}(S)$, the convex hull of $S$. This is a fundamental problem in computational geometry and linear programming. First, we prove: $p \\in {\\rm Conv}(S)$ if and only if for each $p' \\in {\\rm Conv}(S) - \\{p \\}$ there exists $v_j \\in S$ such that the Euclidean distance inequality $d(p',v_j) > d(p,v_j)$ holds. Next, we describe a fully polynomial time approximation scheme: given $\\epsilon >0$ in $O(mn\\epsilon^{-2})$ arithmetic operations it computes $p' \\in {\\rm Conv}(S)$ such that either $d(p', p) \\leq \\epsilon d(p,v_j)$ for some $j$, or $d(p',v_i) < d(p,v_i)$ for all $i=1, ..., n$. In the latter case the hyperplane that orthogonally bisects the line $pp'$ separates $p$ from ${\\rm Conv}(S)$. We also show how to solve linear programming via this approximation algorithm and give a corresponding complexity analysis.
NP-hardness of deciding convexity of quartic polynomials and related problems
Ahmadi, Amir Ali
We show that unless P = NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves ...
Convex optimization of MRI exposure for mitigation of RF-heating from active medical implants
NASA Astrophysics Data System (ADS)
Córcoles, Juan; Zastrow, Earl; Kuster, Niels
2015-09-01
Local RF-heating of elongated medical implants during magnetic resonance imaging (MRI) may pose a significant health risk to patients. The actual patient risk depends on various parameters including RF magnetic field strength and frequency, MR coil design, patient’s anatomy, posture, and imaging position, implant location, RF coupling efficiency of the implant, and the bio-physiological responses associated with the induced local heating. We present three constrained convex optimization strategies that incorporate the implant’s RF-heating characteristics, for the reduction of local heating of medical implants during MRI. The study emphasizes the complementary performances of the different formulations. The analysis demonstrates that RF-induced heating of elongated metallic medical implants can be carefully controlled and balanced against MRI quality. A reduction of heating of up to 25 dB can be achieved at the cost of reduced uniformity in the magnitude of the B1+ field of less than 5%. The current formulations incorporate a priori knowledge of clinically-specific parameters, which is assumed to be available. Before these techniques can be applied practically in the broader clinical context, further investigations are needed to determine whether reduced access to a priori knowledge regarding, e.g. the patient’s anatomy, implant routing, RF-transmitter, and RF-implant coupling, can be accepted within reasonable levels of uncertainty.
An optimal algorithm for ressource allocation problem in concave context A. Le Poupon and O. Rioul
Rioul, Olivier
-optimal results because the optimal solution does not necessarily lie on the convex hull in the A-B plane (see fig on the convex hull are joigned by a segment of slope . The Shoham-Gersho procedure [1] finds a point on the convex hull as the path corresponding to the whole sequence of multipliers 1 2 Â· Â· Â· M . We propose
convex segmentation and mixed-integer footstep planning for a walking robot
Deits, Robin L. H. (Robin Lloyd Henderson)
2014-01-01
This work presents a novel formulation of the footstep planning problem as a mixed-integer convex optimization. The footstep planning problem involves choosing a set of footstep locations which a walking robot can follow ...
Some global optimization problems on Stiefel manifolds ?
Csendes, Tibor
Some global optimization problems on Stiefel manifolds ? J. Balogh #3; Department of Computer was discussed by Rapcs#19;ak in earlier papers, and some global optimization methods were considered and tested the original one to a smooth nonlinear optimization problem. Then, by using Riemannian geometry and the global
Glineur, François
-order information on two usual first-order methods: Classical Gradient Method (CGM) and Fast Gradient Method (FGM2 2 (i.e. a whole family of oracles with arbitrary value of ) Consequence: Application of CGM or FGM 1- 1+ . Consequence: Application of FGM to f with right choice of solves 'weakly' smooth problem
Social Emotional Optimization Algorithm for Nonlinear Constrained Optimization Problems
NASA Astrophysics Data System (ADS)
Xu, Yuechun; Cui, Zhihua; Zeng, Jianchao
Nonlinear programming problem is one important branch in operational research, and has been successfully applied to various real-life problems. In this paper, a new approach called Social emotional optimization algorithm (SEOA) is used to solve this problem which is a new swarm intelligent technique by simulating the human behavior guided by emotion. Simulation results show that the social emotional optimization algorithm proposed in this paper is effective and efficiency for the nonlinear constrained programming problems.
Random test examples with known minimum for convex semi-infinite programming problems
PolitÃ¨cnica de Catalunya, Universitat
, e-mail: eva.miranda@upc.edu. Her research is partially supported by the project GEOMETRIA ALGEBRAICA Eva Miranda May 6, 2013 Abstract A significant research activity has occurred in the area of convex by the Ministerio de Ciencia y TecnologÂ´ia, Project MTM2011-29064-C03-01 Departament de Matem`atica Aplicada I
First and Second Order Necessary Conditions for Stochastic Optimal Control Problems
Bonnans, J. Frederic; Silva, Francisco J.
2012-06-15
In this work we consider a stochastic optimal control problem with either convex control constraints or finitely many equality and inequality constraints over the final state. Using the variational approach, we are able to obtain first and second order expansions for the state and cost function, around a local minimum. This fact allows us to prove general first order necessary condition and, under a geometrical assumption over the constraint set, second order necessary conditions are also established. We end by giving second order optimality conditions for problems with constraints on expectations of the final state.
Constrained Graph Optimization: Interdiction and Preservation Problems
Schild, Aaron V
2012-07-30
The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.
Neumaier, Arnold
algorithm exploits the convex hull relaxation for the discrete search, and the fact that the spatial branch variables, the convex hull of each nonlinear disjunction is constructed. The relaxed convex GDP problem. Keywords: Nonconvex GDP, nonconvex MINLP, convex hull relaxation, branch and bound, global optimization
A Mathematical Optimization Problem in Bioinformatics
ERIC Educational Resources Information Center
Heyer, Laurie J.
2008-01-01
This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…
EQUILIBRIUM CONSTRAINED OPTIMIZATION PROBLEMS S . I. BIRBIL
Al Hanbali, Ahmad
EQUILIBRIUM CONSTRAINED OPTIMIZATION PROBLEMS S¸ . I. BIRBIL , G. BOUZA , J.B.G. FRENK and G. STILL § July 26, 2004 ABSTRACT. We consider equilibrium constrained optimization problems, which have a general for- mulation that encompasses well-known models such as mathematical programs with equilibrium
Tan, Tiow-Seng Optimal Triangulation Problems
Tan, Tiow Seng
Tan, Tiow-Seng Optimal Triangulation Problems This paper surveys some recent solutions to triangulation problems in 2D plane and surface. In particular, it focuses on three e cient and practical schemes in computing optimal triangulations useful in engineering and scienti c computations, such as nite element
Tan, TiowSeng Optimal Triangulation Problems
Tan, Tiow Seng
Tan, TiowÂSeng Optimal Triangulation Problems This paper surveys some recent solutions to triangulation problems in 2D plane and surface. In particular, it focuses on three efficient and practical schemes in computing optimal triangulations useful in engineering and scientific computations
Problem Solving through an Optimization Problem in Geometry
ERIC Educational Resources Information Center
Poon, Kin Keung; Wong, Hang-Chi
2011-01-01
This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…
A near-optimal heuristic for minimum weight triangulation of convex polygons
Levcopoulos, C.; Krznaric, D.
1997-06-01
A linear-time heuristic for minimum weight triangulation of convex polygons is presented. This heuristic produces a triangulation of length within a factor 1 + {epsilon} from the optimum, where {epsilon} is an arbitrarily small positive constant. This is the first sub-cubic algorithm which guarantees such an approximation factor, and it has interesting applications.
Optimization problems in network connectivity
Panigrahi, Debmalya
2012-01-01
Besides being one of the principal driving forces behind research in algorithmic theory for more than five decades, network optimization has assumed increased significance in recent times with the advent and widespread use ...
A non-penalty recurrent neural network for solving a class of constrained optimization problems.
Hosseini, Alireza
2016-01-01
In this paper, we explain a methodology to analyze convergence of some differential inclusion-based neural networks for solving nonsmooth optimization problems. For a general differential inclusion, we show that if its right hand-side set valued map satisfies some conditions, then solution trajectory of the differential inclusion converges to optimal solution set of its corresponding in optimization problem. Based on the obtained methodology, we introduce a new recurrent neural network for solving nonsmooth optimization problems. Objective function does not need to be convex on R(n) nor does the new neural network model require any penalty parameter. We compare our new method with some penalty-based and non-penalty based models. Moreover for differentiable cases, we implement circuit diagram of the new neural network. PMID:26519931
Large Scale Computational Problems in Numerical Optimization
coleman, thomas f.
2000-07-01
Our work under this support broadly falls into five categories: automatic differentiation, sparsity, constraints, parallel computation, and applications. Automatic Differentiation (AD): We developed strong practical methods for computing sparse Jacobian and Hessian matrices which arise frequently in large scale optimization problems [10,35]. In addition, we developed a novel view of "structure" in applied problems along with AD techniques that allowed for the efficient application of sparse AD techniques to dense, but structured, problems. Our AD work included development of freely available MATLAB AD software. Sparsity: We developed new effective and practical techniques for exploiting sparsity when solving a variety of optimization problems. These problems include: bound constrained problems, robust regression problems, the null space problem, and sparse orthogonal factorization. Our sparsity work included development of freely available and published software [38,39]. Constraints: Effectively handling constraints in large scale optimization remains a challenge. We developed a number of new approaches to constrained problems with emphasis on trust region methodologies. Parallel Computation: Our work included the development of specifically parallel techniques for the linear algebra tasks underpinning optimization algorithms. Our work contributed to the nonlinear least-squares problem, nonlinear equations, triangular systems, orthogonalization, and linear programming. Applications: Our optimization work is broadly applicable across numerous application domains. Nevertheless we have specifically worked in several application areas including molecular conformation, molecular energy minimization, computational finance, and bone remodeling.
Analog Processor To Solve Optimization Problems
NASA Technical Reports Server (NTRS)
Duong, Tuan A.; Eberhardt, Silvio P.; Thakoor, Anil P.
1993-01-01
Proposed analog processor solves "traveling-salesman" problem, considered paradigm of global-optimization problems involving routing or allocation of resources. Includes electronic neural network and auxiliary circuitry based partly on concepts described in "Neural-Network Processor Would Allocate Resources" (NPO-17781) and "Neural Network Solves 'Traveling-Salesman' Problem" (NPO-17807). Processor based on highly parallel computing solves problem in significantly less time.
Heuristic Kalman algorithm for solving optimization problems.
Toscano, Rosario; Lyonnet, Patrick
2009-10-01
The main objective of this paper is to present a new optimization approach, which we call heuristic Kalman algorithm (HKA). We propose it as a viable approach for solving continuous nonconvex optimization problems. The principle of the proposed approach is to consider explicitly the optimization problem as a measurement process designed to produce an estimate of the optimum. A specific procedure, based on the Kalman method, was developed to improve the quality of the estimate obtained through the measurement process. The efficiency of HKA is evaluated in detail through several nonconvex test problems, both in the unconstrained and constrained cases. The results are then compared to those obtained via other metaheuristics. These various numerical experiments show that the HKA has very interesting potentialities for solving nonconvex optimization problems, notably concerning the computation time and the success ratio. PMID:19336312
Convex Formulations of Learning from Crowds
NASA Astrophysics Data System (ADS)
Kajino, Hiroshi; Kashima, Hisashi
It has attracted considerable attention to use crowdsourcing services to collect a large amount of labeled data for machine learning, since crowdsourcing services allow one to ask the general public to label data at very low cost through the Internet. The use of crowdsourcing has introduced a new challenge in machine learning, that is, coping with low quality of crowd-generated data. There have been many recent attempts to address the quality problem of multiple labelers, however, there are two serious drawbacks in the existing approaches, that are, (i) non-convexity and (ii) task homogeneity. Most of the existing methods consider true labels as latent variables, which results in non-convex optimization problems. Also, the existing models assume only single homogeneous tasks, while in realistic situations, clients can offer multiple tasks to crowds and crowd workers can work on different tasks in parallel. In this paper, we propose a convex optimization formulation of learning from crowds by introducing personal models of individual crowds without estimating true labels. We further extend the proposed model to multi-task learning based on the resemblance between the proposed formulation and that for an existing multi-task learning model. We also devise efficient iterative methods for solving the convex optimization problems by exploiting conditional independence structures in multiple classifiers.
Convex Interpolation for Gradient Dynamic Programming
NASA Astrophysics Data System (ADS)
Foufoula-Georgiou, Efi
1991-01-01
Local approximation of functions based on values and derivatives at the nodes of a discretized grid are often used in solving problems numerically for which analytical solutions do not exist. In gradient dynamic programming (Foufoula-Georgiou and Kitanidis, 1988) the use of such functions for the approximation of the cost-to-go function alleviates the "curse of dimensionality" by reducing the number of discretization nodes per state while obtaining high-accuracy solutions. Also, efficient Newton-type schemes can be used for the stage-wise optimization, since now the approximation functions have continuous first derivatives. Our interest is in the case where the cost-to-go function is convex. However, the interpolants may not always be convex, introducing numerical problems. In this paper we address the problem of interpolating nodal values and derivatives of a one-dimensional convex function with a convex interpolant so that potential computational difficulties due to approximation-induced nonconvexity are avoided, and an efficient convergence to global instead of local optimal controls is guaranteed at every single-stage optimization.
THE EXACT FEASIBILITY OF RANDOMIZED SOLUTIONS OF UNCERTAIN CONVEX PROGRAMS
Garatti, Simone
-supported problems. Key words. Uncertain Optimization, Randomized Methods, Convex Optimization, Semi- Infinite "Identification and adaptive control of indus- trial systems". Universit`a di Brescia - Dipartimento di://home.dei.polimi.it/sgaratti/ 1 #12;2 M.C. CAMPI AND S. GARATTI effect gave birth to the chance-constrained approach. See also [21
Tracking local optimality for cost parameterized optimization problems
NASA Astrophysics Data System (ADS)
Kuo, Yueh-Cheng; Lee, Tsung-Lin
2014-02-01
In this paper, a procedure for computing local optimal solution curves of the cost parameterized optimization problem is presented. We recast the problem to a parameterized nonlinear equation derived from its Lagrange function and show that the point where the positive definiteness of the projected Hessian matrix vanishes must be a bifurcation point on the solution curve of the equation. Based on this formulation, the local optimal curves can be traced by the continuation method, coupled with the testing of singularity of the Jacobian matrix. Using the proposed procedure, we successfully compute the energy diagram of rotating Bose-Einstein condensates.
Optimal control for problems with a general variational inequality
Optimal control for problems with a general variational study first order optimality conditions for the control of a system* * by a general variational [13] . The control problem as an optimization problem * *is also refered to as generalized bilevel
Modeling Strategic Optimization Criteria in Spatial Combinatorial Optimization Problems.
Perelman, Brandon; Mueller, Shane
2015-09-01
In many real-world route planning and search tasks, humans must solve a combinatorial optimization problem that holds many similarities to the Euclidean Traveling Salesman Problem (TSP). The problem spaces used in real-world tasks differ most starkly from traditional TSP in terms of optimization criteria - Whereas the traditional TSP asks participants to connect all of the nodes to produce the solution that minimizes overall path length, real-world search tasks are often conducted with the goal of minimizing the duration of time required to find the target (i.e., the average distance between nodes). Traditional modeling approaches to TSP assume that humans solve these problems using intrinsic characteristics of the brain and perceptual system (e.g., hierarchical structure in the visual system). A consequence of these approaches is that they are not robust to strategic changes in the aforementioned optimization criteria during path planning. To investigate performance in these tasks, 28 participants solved 18 randomly-presented computer-based combinatorial optimization problems with two sets of task instructions, one designed to encourage shortest-path solutions and the other to encourage solutions that minimized the estimated time to find a target hidden among the nodes (i.e., locations). The node distributions were designed to discriminate between these two strategies. In nearly every case, participants were capable of strategically adapting optimization criteria based on instruction alone. These results indicate the importance of modeling cognition in behaviors that are traditionally thought to be driven automatically by perceptual processes. In addition, we discuss computational models that we have developed to produce optimization criteria-specific solutions to these combinatorial optimization problems using a strategic optimization parameter to guide solutions using a single underlying mechanism. Such models have applications in approximating human behavior in real-world tasks. Meeting abstract presented at VSS 2015. PMID:26326160
Belief Propagation Algorithm for Portfolio Optimization Problems
2015-01-01
The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti et al. [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm. PMID:26305462
Asynchronous Convex Hull Consensus in the Presence of Crash Faults
Vaidya, Nitin
approximate convex hull consensus algorithm with optimal fault tolerance that reaches consen- sus]: [Distributed applications] General Terms Algorithm, Theory Keywords Convex hull consensus, vector inputsAsynchronous Convex Hull Consensus in the Presence of Crash Faults Lewis Tseng Department
Automated segmentation of CBCT image using spiral CT atlases and convex optimization.
Wang, Li; Chen, Ken Chung; Shi, Feng; Liao, Shu; Li, Gang; Gao, Yaozong; Shen, Steve G F; Yan, Jin; Lee, Philip K M; Chow, Ben; Liu, Nancy X; Xia, James J; Shen, Dinggang
2013-01-01
Cone-beam computed tomography (CBCT) is an increasingly utilized imaging modality for the diagnosis and treatment planning of the patients with craniomaxillofacial (CMF) deformities. CBCT scans have relatively low cost and low radiation dose in comparison to conventional spiral CT scans. However, a major limitation of CBCT scans is the widespread image artifacts such as noise, beam hardening and inhomogeneity, causing great difficulties for accurate segmentation of bony structures from soft tissues, as well as separating mandible from maxilla. In this paper, we presented a novel fully automated method for CBCT image segmentation. In this method, we first estimated a patient-specific atlas using a sparse label fusion strategy from predefined spiral CT atlases. This patient-specific atlas was then integrated into a convex segmentation framework based on maximum a posteriori probability for accurate segmentation. Finally, the performance of our method was validated via comparisons with manual ground-truth segmentations. PMID:24505768
Linear stochastic optimal control and estimation problem
NASA Technical Reports Server (NTRS)
Geyser, L. C.; Lehtinen, F. K. B.
1980-01-01
Problem involves design of controls for linear time-invariant system disturbed by white noise. Solution is Kalman filter coupled through set of optimal regulator gains to produce desired control signal. Key to solution is solving matrix Riccati differential equation. LSOCE effectively solves problem for wide range of practical applications. Program is written in FORTRAN IV for batch execution and has been implemented on IBM 360.
Solving Customer-Driven Microgrid Optimization Problems as DCOPs
Yeoh, William
Solving Customer-Driven Microgrid Optimization Problems as DCOPs Saurabh Gupta , Palak Jain common customer-driven microgrid (CDMG) optimization problems a comprehensive CDMG optimization problem. In response to the challenge by Ramchurn et al. to solve smart grid optimization problems with artificial
NASA Astrophysics Data System (ADS)
Crasta, Graziano; Fragalà, Ilaria
2015-12-01
Given an open bounded subset ? of {{R}^n}, which is convex and satisfies an interior sphere condition, we consider the pde {-?_{?} u = 1} in ?, subject to the homogeneous boundary condition u = 0 on ??. We prove that the unique solution to this Dirichlet problem is power-concave (precisely, 3/4 concave) and it is of class C 1( ?). We then investigate the overdetermined Serrin-type problem, formerly considered in Buttazzo and Kawohl (Int Math Res Not, pp 237-247, 2011), obtained by adding the extra boundary condition {|nabla u| = a} on ??; by using a suitable P-function we prove that, if ? satisfies the same assumptions as above and in addition contains a ball which touches ?? at two diametral points, then the existence of a solution to this Serrin-type problem implies that necessarily the cut locus and the high ridge of ? coincide. In turn, in dimension n = 2, this entails that ? must be a stadium-like domain, and in particular it must be a ball in case its boundary is of class C 2.
Ant Algorithms Solve Difficult Optimization Problems
Libre de Bruxelles, Université
Ant Algorithms Solve Difficult Optimization Problems Marco Dorigo IRIDIA Universit´e Libre de Bruxelles 50 Avenue F. Roosevelt B-1050 Brussels, Belgium mdorigo@ulb.ac.be Abstract. The ant algorithms research field builds on the idea that the study of the behavior of ant colonies or other social insects
SIAM J. OPTIM. c 2005 Society for Industrial and Applied Mathematics Vol. 15, No. 3, pp. 780804
Bertsimas, Dimitris
inequalities, we obtain an improving sequence of bounds by solving semidefinite optimization problems by solving n convex optimization problems when the set S is convex, and we provide a polynomial time on optimization methods to address in a unified manner moment-inequality problems in probability theory
Model results of optimized convex shapes for a solar thermal rocket thruster
Cartier, S.L.
1995-11-01
A computational, 3-D model for evaluating the performance of solar thermal thrusters is under development. The model combines Monte-Carlo and ray-tracing techniques to follow the ray paths of concentrated solar radiation through an axially symmetric heat-exchanger surface for both convex and concave cavity shapes. The enthalpy of a propellant, typically hydrogen gas, increases as it flows over the outer surface of the absorber/exchanger cavity. Surface temperatures are determined by the requirement that the input radiant power to surface elements balance with the reradiated power and heat conducted to the propellant. The model uses tabulated forms of surface emissivity and gas enthalpy. Temperature profiles result by iteratively calculating surface and propellant temperatures until the solutions converge to stable values. The model provides a means to determine the effectiveness of incorporating a secondary concentrator into the heat-exchanger cavity. A secondary concentrator increases the amount of radiant energy entering the cavity. The model will be used to evaluate the data obtained from upcoming experiments. Characteristics of some absorber/exchanger cavity shapes combined with optionally attached conical secondary concentrators for various propellant flow rates are presented. In addition, shapes that recover some of the diffuse radiant energy which would otherwise not enter the secondary concentrator are considered.
Quasi-Newton Algorithms for Non-smooth Online Strongly Convex Optimization
Godwin, Mark Franklin
2011-01-01
ONLINE PORTFOLIO OPTIMIZATION To gain insight into the algorithms’ strategies we run numerical experiments with a portfolio of Coke,Coke, IBM and GE Algorithm FTAL-OPO FTAL-SC UCRP Wealth APY Volatility CHAPTER 5. ONLINE
Noether's Theorem for Fractional Optimal Control Problems
Gastao S. F. Frederico; Delfim F. M. Torres
2006-03-25
We begin by reporting on some recent results of the authors (Frederico and Torres, 2006), concerning the use of the fractional Euler-Lagrange notion to prove a Noether-like theorem for the problems of the calculus of variations with fractional derivatives. We then obtain, following the Lagrange multiplier technique used in (Agrawal, 2004), a new version of Noether's theorem to fractional optimal control systems.
Phase retrieval, error reduction algorithm, and Fienup variants: A view from convex optimization
Luke, D. Russell
is of paramount importance in various areas of applied physics and engineering. The state of the art for solving numerical scheme to solve this type of problem. While its intrinsic mechanism is clear physically¨ottingen 37083 G¨ottingen, Germany. January 14, 2002 version 1.29 Abstract The phase retrieval problem
Simultaneous Optimization via Approximate Majorization for Concave Profits or Convex Costs
Meyerson, Adam W.
For multi-criteria problems and problems with poorly characterized objective, it is often desirable of bandwidths in a computer network). The concavity requirement corresponds to the law of diminishing returns corresponds to the "law of diminishing returns" from economics. Symmetry corresponds to saying that all users
Simultaneous Optimization via Approximate Majorization for Concave Profits or Convex Costs
Goel, Ashish
Abstract For multi-criteria problems and problems with poorly characterized objective, it is often to the law of diminishing returns in economics. The second class corresponds to minimizing cost or congestion of the objective function corresponds to the "law of diminishing returns" from economics. Symmetry corresponds
Exact Matrix Completion via Convex Optimization Emmanuel J. Cand`es
Qiu, Robert Caiming
would like to be able to recover a low-rank matrix from a sampling of its entries. · The Netflix problem is the now famous Netflix problem [2]. Users (rows of the data matrix) are given the opportunity to rate that the vendor (here Netflix) might recommend titles that any particular user is likely to be willing to order
Wang, Yong; Li, Han-Xiong; Yen, Gary G; Song, Wu
2015-04-01
In the field of evolutionary computation, there has been a growing interest in applying evolutionary algorithms to solve multimodal optimization problems (MMOPs). Due to the fact that an MMOP involves multiple optimal solutions, many niching methods have been suggested and incorporated into evolutionary algorithms for locating such optimal solutions in a single run. In this paper, we propose a novel transformation technique based on multiobjective optimization for MMOPs, called MOMMOP. MOMMOP transforms an MMOP into a multiobjective optimization problem with two conflicting objectives. After the above transformation, all the optimal solutions of an MMOP become the Pareto optimal solutions of the transformed problem. Thus, multiobjective evolutionary algorithms can be readily applied to find a set of representative Pareto optimal solutions of the transformed problem, and as a result, multiple optimal solutions of the original MMOP could also be simultaneously located in a single run. In principle, MOMMOP is an implicit niching method. In this paper, we also discuss two issues in MOMMOP and introduce two new comparison criteria. MOMMOP has been used to solve 20 multimodal benchmark test functions, after combining with nondominated sorting and differential evolution. Systematic experiments have indicated that MOMMOP outperforms a number of methods for multimodal optimization, including four recent methods at the 2013 IEEE Congress on Evolutionary Computation, four state-of-the-art single-objective optimization based methods, and two well-known multiobjective optimization based approaches. PMID:25099966
Analysis of the Optimal Relaxed Control to an Optimal Control Problem
Lou Hongwei
2009-02-15
Relaxed controls are widely used to analyze the existence of optimal controls in the literature. Though there are many optimal control problems admitting no optimal control, rare examples were shown. This paper will solve a particular optimal control problem by analyzing the optimal relaxed controls, showing the ideas we used to study such kind of problems.
Chen, Yunjie; Zhao, Bo; Zhang, Jianwei; Zheng, Yuhui
2014-09-01
Accurate segmentation of magnetic resonance (MR) images remains challenging mainly due to the intensity inhomogeneity, which is also commonly known as bias field. Recently active contour models with geometric information constraint have been applied, however, most of them deal with the bias field by using a necessary pre-processing step before segmentation of MR data. This paper presents a novel automatic variational method, which can segment brain MR images meanwhile correcting the bias field when segmenting images with high intensity inhomogeneities. We first define a function for clustering the image pixels in a smaller neighborhood. The cluster centers in this objective function have a multiplicative factor that estimates the bias within the neighborhood. In order to reduce the effect of the noise, the local intensity variations are described by the Gaussian distributions with different means and variances. Then, the objective functions are integrated over the entire domain. In order to obtain the global optimal and make the results independent of the initialization of the algorithm, we reconstructed the energy function to be convex and calculated it by using the Split Bregman theory. A salient advantage of our method is that its result is independent of initialization, which allows robust and fully automated application. Our method is able to estimate the bias of quite general profiles, even in 7T MR images. Moreover, our model can also distinguish regions with similar intensity distribution with different variances. The proposed method has been rigorously validated with images acquired on variety of imaging modalities with promising results. PMID:24832358
Finding Globally Optimum Solutions in Antenna Optimization Problems
Hajimiri, Ali
Finding Globally Optimum Solutions in Antenna Optimization Problems Aydin Babakhani*, Javad Lavaei, it is worth mentioning that none of the existing antenna optimization techniques provides a globally optimum strongly supported the development of optimization techniques for designing antennas. Among
A Combinatorial Optimal Control Problem for Spacecraft Formation Reconfiguration
Leok, Melvin
A Combinatorial Optimal Control Problem for Spacecraft Formation Reconfiguration Taeyoung Lee a geometrically exact and numerically efficient discrete optimal control method based on Lie group variational attitude dynamics under a central gravitational potential. Thus, finding the optimal control inputs
Numerical Approximations of Stochastic Optimal Stopping and Control Problems
Siska, David
2007-01-01
We study numerical approximations for the payoff function of the stochastic optimal stopping and control problem. It is known that the payoff function of the optimal stopping and control problem corresponds to the solution ...
LDRD Final Report: Global Optimization for Engineering Science Problems
HART,WILLIAM E.
1999-12-01
For a wide variety of scientific and engineering problems the desired solution corresponds to an optimal set of objective function parameters, where the objective function measures a solution's quality. The main goal of the LDRD ''Global Optimization for Engineering Science Problems'' was the development of new robust and efficient optimization algorithms that can be used to find globally optimal solutions to complex optimization problems. This SAND report summarizes the technical accomplishments of this LDRD, discusses lessons learned and describes open research issues.
Stress-based upper-bound method and convex optimization: case of the Gurson material
NASA Astrophysics Data System (ADS)
Pastor, Franck; Trillat, Malorie; Pastor, Joseph; Loute, Etienne
2006-04-01
A nonlinear interior point method associated with the kinematic theorem of limit analysis is proposed. Associating these two tools enables one to determine an upper bound of the limit loading of a Gurson material structure from the knowledge of the sole yield criterion. We present the main features of the interior point algorithm and an original method providing a rigorous kinematic bound from a stress formulation of the problem. This method is tested by solving in plane strain the problem of a Gurson infinite bar compressed between rough rigid plates. To cite this article: F. Pastor et al., C. R. Mecanique 334 (2006).
Optimal Planning and Problem-Solving
NASA Technical Reports Server (NTRS)
Clemet, Bradley; Schaffer, Steven; Rabideau, Gregg
2008-01-01
CTAEMS MDP Optimal Planner is a problem-solving software designed to command a single spacecraft/rover, or a team of spacecraft/rovers, to perform the best action possible at all times according to an abstract model of the spacecraft/rover and its environment. It also may be useful in solving logistical problems encountered in commercial applications such as shipping and manufacturing. The planner reasons around uncertainty according to specified probabilities of outcomes using a plan hierarchy to avoid exploring certain kinds of suboptimal actions. Also, planned actions are calculated as the state-action space is expanded, rather than afterward, to reduce by an order of magnitude the processing time and memory used. The software solves planning problems with actions that can execute concurrently, that have uncertain duration and quality, and that have functional dependencies on others that affect quality. These problems are modeled in a hierarchical planning language called C_TAEMS, a derivative of the TAEMS language for specifying domains for the DARPA Coordinators program. In realistic environments, actions often have uncertain outcomes and can have complex relationships with other tasks. The planner approaches problems by considering all possible actions that may be taken from any state reachable from a given, initial state, and from within the constraints of a given task hierarchy that specifies what tasks may be performed by which team member.
Extremal Optimization for Quadratic Unconstrained Binary Problems
NASA Astrophysics Data System (ADS)
Boettcher, S.
We present an implementation of ?-EO for quadratic unconstrained binary optimization (QUBO) problems. To this end, we transform modify QUBO from its conventional Boolean presentation into a spin glass with a random external field on each site. These fields tend to be rather large compared to the typical coupling, presenting EO with a challenging two-scale problem, exploring smaller differences in couplings effectively while sufficiently aligning with those strong external fields. However, we also find a simple solution to that problem that indicates that those external fields apparently tilt the energy landscape to a such a degree such that global minima become more easy to find than those of spin glasses without (or very small) fields. We explore the impact of the weight distribution of the QUBO formulation in the operations research literature and analyze their meaning in a spin-glass language. This is significant because QUBO problems are considered among the main contenders for NP-hard problems that could be solved efficiently on a quantum computer such as D-Wave.
Solving Global Optimization Problems using MANGO Akin Gunay1
Yanikoglu, Berrin
Solving Global Optimization Problems using MANGO Akin G¨unay1 , Figen ¨Oztoprak2 , S¸. Ilker Birbil. Traditional approaches for solving global optimization problems gen- erally rely on a single algorithm to form teams of algorithms to tackle global optimization problems. Each algorithm is embod- ied and ran
Sequential Multiresolution Trajectory Optimization Schemes for Problems with Moving Targets
Tsiotras, Panagiotis
Sequential Multiresolution Trajectory Optimization Schemes for Problems with Moving Targets Sachin.2514/1.37899 In this paper, we present two sequential multiresolution trajectory optimization algorithms for solving problems resolution to solve the associated trajectory optimization problem on a nonuniform grid across time. The grid
Hybrid intelligent optimization methods for engineering problems
NASA Astrophysics Data System (ADS)
Pehlivanoglu, Yasin Volkan
The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients of these increments are essential to search the yield space. However, the landscape of yield is not a simple one and mostly multi-modal. Another issue is differentiability. Engineering design problems are usually nonlinear and they sometimes exhibit discontinuous derivatives for the objective and constraint functions. Due to these difficulties, non-gradient-based algorithms have become more popular in recent decades. Genetic algorithms (GA) and particle swarm optimization (PSO) algorithms are popular, non-gradient based algorithms. Both are population-based search algorithms and have multiple points for initiation. A significant difference from a gradient-based method is the nature of the search methodologies. For example, randomness is essential for the search in GA or PSO. Hence, they are also called stochastic optimization methods. These algorithms are simple, robust, and have high fidelity. However, they suffer from similar defects, such as, premature convergence, less accuracy, or large computational time. The premature convergence is sometimes inevitable due to the lack of diversity. As the generations of particles or individuals in the population evolve, they may lose their diversity and become similar to each other. To overcome this issue, we studied the diversity concept in GA and PSO algorithms. Diversity is essential for a healthy search, and mutations are the basic operators to provide the necessary variety within a population. After having a close scrutiny of the diversity concept based on qualification and quantification studies, we improved new mutation strategies and operators to provide beneficial diversity within the population. We called this new approach as multi-frequency vibrational GA or PSO. They were applied to different aeronautical engineering problems in order to study the efficiency of these new approaches. These implementations were: applications to selected benchmark test functions, inverse design of two-dimensional (2D) airfoil in subsonic flow, optimization of 2D airfoil in transonic flow, path planning problems of autonomous unmanned aerial vehicle (UAV) over a 3D terrain environment, 3D radar cross section minimization problem for a 3D air vehicle, and active flow control over a 2D airfoil. As demonstrated by these test cases, we observed that new algorithms outperform the current popular algorithms. The principal role of this multi-frequency approach was to determine which individuals or particles should be mutated, when they should be mutated, and which ones should be merged into the population. The new mutation operators, when combined with a mutation strategy and an artificial intelligent method, such as, neural networks or fuzzy logic process, they provided local and global diversities during the reproduction phases of the generations. Additionally, the new approach also introduced random and controlled diversity. Due to still being population-based techniques, these methods were as robust as the plain GA or PSO algorithms. Based on the results obtained, it was concluded that the variants of the present multi-frequency vibrational GA and PSO were efficient algorithms, since they successfully avoided all local optima within relatively short optimization cycles.
Finding optimal solutions for generalized quantum state discrimination problems
Kenji Nakahira; Tsuyoshi Sasaki Usuda; Kentaro Kato
2015-10-18
We try to find an optimal quantum measurement for generalized quantum state discrimination problems, which include the problem of finding an optimal measurement maximizing the average correct probability with and without a fixed rate of inconclusive results and the problem of finding an optimal measurement in the Neyman-Pearson strategy. We propose an approach in which the optimal measurement is obtained by solving a modified version of the original problem. In particular, the modified problem can be reduced to one of finding a minimum error measurement for a certain state set, which is relatively easy to solve. We clarify the relationship between optimal solutions to the original and modified problems, with which one can obtain an optimal solution to the original problem in some cases. Moreover, as an example of application of our approach, we present an algorithm for numerically obtaining optimal solutions to generalized quantum state discrimination problems.
Entanglement quantification made easy: Polynomial measures invariant under convex decomposition
Regula, Bartosz
2015-01-01
Quantifying entanglement in composite systems is a fundamental challenge, yet exact results are only available in few special cases. This is because hard optimization problems are routinely involved, such as finding the convex decomposition of a mixed state with the minimal average pure-state entanglement, the so-called convex roof. We show that under certain conditions such a problem becomes trivial. Precisely, we prove by a geometric argument that polynomial entanglement measures of degree 2 are independent of the choice of pure-state decomposition of a mixed state, when the latter has only one pure unentangled state in its range. This allows for the analytical evaluation of convex roof extended entanglement measures in classes of rank-two states obeying such condition. We give explicit examples for the square root of the three-tangle in three-qubit states, and show that several representative classes of four-qubit pure states have marginals that enjoy this property.
Optimal Auction Design for Agents with Hard Valuation Problems
Chen, Yiling
Optimal Auction Design for Agents with Hard Valuation Problems David C. Parkes ? Computer human expert. Although auction design cannot simplify the valuation problem itself, we show that good. Keywords: agent-mediated electronic commerce, valuation problem, metade- liberation, auction theory
Fast Approximate Convex Decomposition
Ghosh, Mukulika
2012-10-19
Approximate convex decomposition (ACD) is a technique that partitions an input object into "approximately convex" components. Decomposition into approximately convex pieces is both more efficient to compute than exact convex decomposition and can...
NASA Technical Reports Server (NTRS)
Nguyen, Duc T.
1990-01-01
Practical engineering application can often be formulated in the form of a constrained optimization problem. There are several solution algorithms for solving a constrained optimization problem. One approach is to convert a constrained problem into a series of unconstrained problems. Furthermore, unconstrained solution algorithms can be used as part of the constrained solution algorithms. Structural optimization is an iterative process where one starts with an initial design, a finite element structure analysis is then performed to calculate the response of the system (such as displacements, stresses, eigenvalues, etc.). Based upon the sensitivity information on the objective and constraint functions, an optimizer such as ADS or IDESIGN, can be used to find the new, improved design. For the structural analysis phase, the equation solver for the system of simultaneous, linear equations plays a key role since it is needed for either static, or eigenvalue, or dynamic analysis. For practical, large-scale structural analysis-synthesis applications, computational time can be excessively large. Thus, it is necessary to have a new structural analysis-synthesis code which employs new solution algorithms to exploit both parallel and vector capabilities offered by modern, high performance computers such as the Convex, Cray-2 and Cray-YMP computers. The objective of this research project is, therefore, to incorporate the latest development in the parallel-vector equation solver, PVSOLVE into the widely popular finite-element production code, such as the SAP-4. Furthermore, several nonlinear unconstrained optimization subroutines have also been developed and tested under a parallel computer environment. The unconstrained optimization subroutines are not only useful in their own right, but they can also be incorporated into a more popular constrained optimization code, such as ADS.
Toussaint, Godfried T.
. Preparata, ``Approximation algorithms for convex hulls,'' Comm. ACM 25 (January 1982), 64Â68. [24] S. G. Akl and G. T. Toussaint, ``A fast algorithm for the planar convex hull problem,'' inÂ ternal manuscript timeÂandÂstorage efficient implementation of an optimal planar convex hull algorithm,'' Technical
NASA Astrophysics Data System (ADS)
Ju, Wenqi; Luo, Jun
Given a set of n equal size and non-overlapping axis-aligned squares, we need to choose exactly one point in each square to make the area of a convex hull of the resulting point set as large as possible. Previous algorithm [10] on this problem gives an optimal algorithm with O(n 3) running time. In this paper, we propose an approximation algorithm which runs in O(nlogn) time and gives a convex hull with area larger than the area of the optimal convex hull minus the area of one square.
Optimization of evacuation instructions as a fixed-point problem
Bierlaire, Michel
Optimization of evacuation instructions as a fixed- point problem Olga Huibregtse Gunnar Flötteröd Michel Bierlaire Andreas Hegyi Serge Hoogendoorn STRC 2011 May 2011 #12;Optimization of evacuation instructions as a fixed-point problem May 2011 STRC 2011 Optimization of evacuation instructions as a fixed
A global optimization method for nonlinear bilevel programming problems.
Amouzegar, M A
1999-01-01
Nonlinear two-level programming deals with optimization problems in which the constraint region is implicitly determined by another optimization problem. Mathematical programs of this type arise in connection with policy problems to which the Stackelberg leader-follower game is applicable. In this paper, the nonlinear bilevel programming problem is restated as a global optimization problem and a new solution method based on this approach is developed. The most important feature of this new method is that it attempts to take full advantage of the structure in the constraints using some recent global optimization techniques. PMID:18252356
Semard, Gaëlle; Peulon-Agasse, Valerie; Bruchet, Auguste; Bouillon, Jean-Philippe; Cardinaël, Pascal
2010-08-13
It is important to develop methods of optimizing the selection of column sets and operating conditions for comprehensive two-dimensional gas chromatography. A new method for the calculation of the percentage of separation space used was developed using Delaunay's triangulation algorithms (convex hull). This approach was compared with an existing method and showed better precision and accuracy. It was successfully applied to the selection of the most convenient column set and the geometrical parameters of second column for the analysis of 49 target compounds in wastewater. PMID:20633886
Mesh refinement strategy for optimal control problems
NASA Astrophysics Data System (ADS)
Paiva, L. T.; Fontes, F. A. C. C.
2013-10-01
Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform nodes collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. After computing a solution in a coarse mesh, the local error is evaluated, which gives information about the subintervals of time domain where refinement is needed. This procedure is repeated until the local error reaches a user-specified threshold. The technique is applied to solve the car-like vehicle problem aiming minimum consumption. The approach developed in this paper leads to results with greater accuracy and yet with lower overall computational time as compared to using a time meshes having equidistant spacing.
Genetic Algorithms for Combinatorial Optimization: The Assembly Line Balancing Problem
Ferris, Michael C.
Genetic Algorithms for Combinatorial Optimization: The Assembly Line Balancing Problem Edward J optimization. We consider the application of the genetic algorithm to a particular problem, the Assembly Line Balancing Problem. A general description of genetic algorithms is given, and their specialized use on our
Optimization with extremal dynamics for the traveling salesman problem
NASA Astrophysics Data System (ADS)
Chen, Yu-Wang; Lu, Yong-Zai; Chen, Peng
2007-11-01
By mapping the optimization problems to physical systems, the paper presents a general-purpose stochastic optimization method with extremal dynamics. It is built up with the traveling salesman problem (TSP) being a typical NP-complete problem. As self-organized critical processes of extremal dynamics, the optimization dynamics successively updates the states of those cities with high energy. Consequently, a near-optimal solution can be quickly obtained through the optimization processes combining the two phases of greedy searching and fluctuated explorations (ergodic walk near the phase transition). The computational results demonstrate that the proposed optimization method may provide much better performance than other optimization techniques developed from statistical physics, such as simulated annealing (SA). Since the proposed fundamental solution is based on the principles and micromechanisms of computational systems, it can provide systematic viewpoints and effective computational methods on a wide spectrum of combinatorial and physical optimization problems.
First-order convex feasibility algorithms for x-ray CT
Sidky, Emil Y.; Pan Xiaochuan; Jorgensen, Jakob S.
2013-03-15
Purpose: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution-thereby facilitating the IIR algorithm design process. Methods: An accelerated version of the Chambolle-Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization. Results: The accelerated CP algorithms are demonstrated on a simulation of circular fan-beam CT with a limited scanning arc of 144 Degree-Sign . The CP algorithms are seen in the empirical results to converge to the solution of their respective convex feasibility problems. Conclusions: Formulation of convex feasibility problems can provide a useful alternative to unconstrained optimization when designing IIR algorithms for CT. The approach is amenable to recent methods for accelerating first-order algorithms which may be particularly useful for CT with limited angular-range scanning. The present paper demonstrates the methodology, and future work will illustrate its utility in actual CT application.
An Inverse Optimality Method to Solve a Class of Optimal Control Problems
Henrion, Didier
An Inverse Optimality Method to Solve a Class of Optimal Control Problems Luis Rodrigues1 , Didier the running cost that renders the control input optimal is also explicitly determined. One special feature and obtaining an optimal controller for the same class of systems using a specific optimization functional. We
Toussaint, Godfried T.
. Preparata, "Approximation algorithms for convex hulls," Comm. ACM 25 (January 1982), 64-68. [24] S. G. Akl and G. T. Toussaint, "A fast algorithm for the planar convex hull problem," in- ternal manuscript-and-storage efficient implementation of an optimal planar convex hull algorithm," Technical Report No. SOCS 81
A Simple But Effective Evolutionary Algorithm for Complicated Optimization Problems
Xu, Y.G.
A simple but effective evolutionary algorithm is proposed in this paper for solving complicated optimization problems. The new algorithm presents two hybridization operations incorporated with the conventional genetic ...
Approximate Designs for Linear Regression: Invariance, Admissibility, and Optimality
Magdeburg, UniversitÃ¤t
, but the side conditions are given as a convex hull of some (infinite) generator. Such side conditions seem is a difficult problem. In the approximate theory the related optimization problems possess convex structures a combination of both reduction concepts can be used for developing a highly efficient and fast algorithm
Weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1991-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
A weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1990-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
A weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1989-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Maximum margin classification based on flexible convex hulls for fault diagnosis of roller bearings
NASA Astrophysics Data System (ADS)
Zeng, Ming; Yang, Yu; Zheng, Jinde; Cheng, Junsheng
2016-01-01
A maximum margin classification based on flexible convex hulls (MMC-FCH) is proposed and applied to fault diagnosis of roller bearings. In this method, the class region of each sample set is approximated by a flexible convex hull of its training samples, and then an optimal separating hyper-plane that maximizes the geometric margin between flexible convex hulls is constructed by solving a closest pair of points problem. By using the kernel trick, MMC-FCH can be extended to nonlinear cases. In addition, multi-class classification problems can be processed by constructing binary pairwise classifiers as in support vector machine (SVM). Actually, the classical SVM also can be regarded as a maximum margin classification based on convex hulls (MMC-CH), which approximates each class region with a convex hull. The convex hull is a special case of the flexible convex hull. To train a MMC-FCH classifier, time-domain and frequency-domain statistical parameters are extracted not only from raw vibration signals but also from the resulting intrinsic mode functions (IMFs) by performing empirical mode decomposition (EMD) on the raw signals, and then the distance evaluation technique (DET) is used to select salient features from the whole statistical features. The experiments on bearing datasets show that the proposed method can reliably recognize different bearing faults.
Neumaier, Arnold
HIGHLIGHT Advances in Global Optimization Optimization problems are ubiquitous and extremely, geophysics, industrial technology, and economics. The formulation of the Global Optimization Problem (GOP accurate results than previously reported global optimization techniques. To further advance
Combinatorial optimization problems with normal random costs Paolo Serafini
Serafini, Paolo
, Department of Mathematics and Computer Science Abstract. We consider combinatorial optimization problems the following general definition of a combinatorial optimization problem: a finite set E and a family X according to this definition. In this paper we consider the extension of the previous definition to the case
A Genetic Algorithm for Minimax Optimization Problems Jeffrey W. Herrmann
Herrmann, Jeffrey W.
A Genetic Algorithm for Minimax Optimization Problems Jeffrey W. Herrmann Department of Mechanical-space genetic algorithm as a general technique to solve minimax optimization problems. This algorithm maintains of applications. To illustrate its potential, we use the two-space genetic algorithm to solve a parallel machine
The Role of Intuition in the Solving of Optimization Problems
ERIC Educational Resources Information Center
Malaspina, Uldarico; Font, Vicenc
2010-01-01
This article presents the partial results obtained in the first stage of the research, which sought to answer the following questions: (a) What is the role of intuition in university students' solutions to optimization problems? (b) What is the role of rigor in university students' solutions to optimization problems? (c) How is the combination of…
Verified Solution of Large Systems and Global Optimization Problems
Rump, Siegfried M.
on the solution of large, banded or sparse systems and on global uncon- strained optimization problems including. For example, if in Gaussian elimination with pivoting the pivot becomes a number with an error bound so big and with sparse Jacobian and to global optimization problems. Theory and algorithms for many other standard
Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem
NASA Astrophysics Data System (ADS)
Chen, Wei
2015-07-01
In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.
Mathematical formulation of technological processes optimization problem
NASA Astrophysics Data System (ADS)
Stupina, A. A.; Shigina, A. A.; Shigin, A. O.
2015-10-01
In this article the methodological principles of creation of adequate mathematical models of the technological processes, which are focused on the use in the tasks of optimization. In this article the task multiobjective parameter optimization formulates at with several control variables in the conditions of uncertainty is considered. Minimizing measurement errors requires introduction to technical system of an adaptive element, which allows it to consider some uncertainty during modeling and optimization.
Optimal Sum-Rate of the Vector Gaussian CEO Problem
Ekrem, Ersen
2012-01-01
We study the vector Gaussian CEO problem, and obtain the optimal sum-rate that attains any given distortion. We show that the evaluation of the Berger-Tung inner bound with jointly Gaussian auxiliary random variables is optimal. We prove this optimality result by using channel enhancement in conjunction with a recent outer bound for the rate-distortion region of the vector Gaussian CEO problem.
GimÃ©nez, Domingo
Motivation Optimization scheme The problem Running conditions Tools Experiments Conclusions 2009 #12;Motivation Optimization scheme The problem Running conditions Tools Experiments Conclusions Contents 1 Motivation 2 Optimization scheme 3 The problem 4 Running conditions 5 Tools 6 Experiments 7
A Smooth Regularization of the Projection Formula for Constrained Parabolic Optimal Control Problems
Nabben, Reinhard
A Smooth Regularization of the Projection Formula for Constrained Parabolic Optimal Control parabolic optimal control problems. We summarize the optimality conditions in function spaces numerical results for an example problem. 1 Introduction Optimal control problems (OCPs) subject to time
Magdeburg, UniversitÃ¤t
of a * Vector Trajectorial Discrete Optimization Problem E. Girlich discrete optimization problem on a system of non- empty subsets (trajectories) of a finite set and MINMIN. The stability of efficient (Pareto optimal, Slater optimal and Smale optim* *al
Improved extremal optimization for the asymmetric traveling salesman problem
NASA Astrophysics Data System (ADS)
Chen, Yu-Wang; Zhu, Yao-Jia; Yang, Gen-Ke; Lu, Yong-Zai
2011-11-01
This paper presents an improved extremal optimization (IEO) algorithm for solving the asymmetric traveling salesman problem (ATSP). At each update step, the IEO algorithm proceeds through two main steps: extremal dynamics and cooperative optimization. As an improvement of extremal optimization (EO), the IEO provides a general combinatorial optimization framework by emphasizing the step of cooperative optimization. In the paper, an effective cooperative optimization strategy with combination of greedy search and random walk is designed in terms of the microscopic characteristics of the ATSP solutions. Simulation results on a set of benchmark ATSP instances show that the proposed IEO algorithm provides satisfactory performance on computational effectiveness and efficiency.
Convex approximation to the likelihood criterion for aperture synthesis imaging.
Meimon, Serge; Mugnier, Laurent M; Le Besnerais, Guy
2005-11-01
Aperture synthesis allows one to measure visibilities at very high resolutions by coupling telescopes of reasonable diameters. We consider the case where visibility amplitudes and phase are measured separately. It leads to an estimation problem where the noise model yields a nonconvex data-likelihood criterion. We show how to optimally approximate the noise model while keeping the criterion convex. This approximation has been validated both on simulations and on experimental data. PMID:16302388
Wu, Xiaodong
2006-01-01
In this paper, we study several interesting optimal-ratio region detection (ORD) problems in d-D (d ? 3) discrete geometric spaces, which arise in high dimensional medical image segmentation. Given a d-D voxel grid of n cells, two classes of geometric regions that are enclosed by a single or two coupled smooth heighfield surfaces defined on the entire grid domain are considered. The objective functions are normalized by a function of the desired regions, which avoids a bias to produce an overly large or small region resulting from data noise. The normalization functions that we employ are used in real medical image segmentation. To our best knowledge, no previous results on these problems in high dimensions are known. We develop a unified algorithmic framework based on a careful characterization of the intrinsic geometric structures and a nontrivial graph transformation scheme, yielding efficient polynomial time algorithms for solving these ORD problems. Our main ideas include the following. We observe that the optimal solution to the ORD problems can be obtained via the construction of a convex hull for a set of O(n) unknown 2-D points using the hand probing technique. The probing oracles are implemented by computing a minimum s-t cut in a weighted directed graph. The ORD problems are then solved by O(n) calls to the minimum s-t cut algorithm. For the class of regions bounded by a single heighfield surface, our further investigation shows that the O(n) calls to the minimum s-t cut algorithm are on a monotone parametric flow network, which enables to detect the optimal-ratio region in the complexity of computing a single maximum flow. PMID:25414538
Introduction Optimal Control Problem 1.1
Grigorieva, Ellina V.
of this Model Environmental Pollution Problem Solving Review of the Literature Game Approach to Manufacturer for Study Environmental Pollution Problem Solving Review of the Literature Game Approach to Manufacturer Reasons for Study Environmental Pollution Problem Solving Review of the Literature Game Approach
introduction first problem two optimization problems in physiology
Combettes, Patrick Louis
proliferates in a diabetic organism? #12;introduction first problem compartmental analysis concept: compartment kinetics' descriptor: exchange coefficients data: FDG (micro)-PET images #12;introduction first problem (micro)-PET images mathematical model: the kinetic input is modeled by an input function which
Optimality conditions for the numerical solution of optimization problems with PDE constraints :
Aguilo Valentin, Miguel Alejandro; Ridzal, Denis
2014-03-01
A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.
Singular perturbation analysis of AOTV-related trajectory optimization problems
NASA Technical Reports Server (NTRS)
Calise, Anthony J.; Bae, Gyoung H.
1990-01-01
The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model.
Optimized Waveform Relaxation Solution of Electromagnetic and Circuit Problems
Gander, Martin J.
1 Optimized Waveform Relaxation Solution of Electromagnetic and Circuit Problems Martin J. Gander element equivalent circuit will yield a powerful technique for solving electromagnetic problems a method for the parallel solution of time domain combined ElectroMagetic (EM) and circuit problems. The EM
GLOBAL OPTIMIZATION FOR THE PHASE AND CHEMICAL EQUILIBRIUM PROBLEM
Neumaier, Arnold
EQUATION Conor M. McDonald and Christodoulos A. Floudas \\Lambda Department of Chemical EngineeringGLOBAL OPTIMIZATION FOR THE PHASE AND CHEMICAL EQUILIBRIUM PROBLEM: APPLICATION TO THE NRTL of solutions to the phase and chemical equilibrium problem when the problem is posed as the minimization
Optimal Control of the Obstacle Problem in a Perforated Domain
Stroemqvist, Martin H.
2012-10-15
We study the problem of optimally controlling the solution of the obstacle problem in a domain perforated by small periodically distributed holes. The solution is controlled by the choice of a perforated obstacle which is to be chosen in such a fashion that the solution is close to a given profile and the obstacle is not too irregular. We prove existence, uniqueness and stability of an optimal obstacle and derive necessary and sufficient conditions for optimality. When the number of holes increase indefinitely we determine the limit of the sequence of optimal obstacles and solutions. This limit depends strongly on the rate at which the size of the holes shrink.
A Planning Problem Combining Calculus of Variations and Optimal Transport
Carlier, G. Lachapelle, A.
2011-02-15
We consider some variants of the classical optimal transport where not only one optimizes over couplings between some variables x and y but also over some control variables governing the evolutions of these variables with time. Such a situation is motivated by an assignment problem of tasks with workers whose characteristics can evolve with time (and be controlled). We distinguish between the coupled and decoupled case. The coupled case is a standard optimal transport with the value of some optimal control problem as cost. The decoupled case is more involved since it is nonlinear in the transport plan.
Comparison of optimal design methods in inverse problems
NASA Astrophysics Data System (ADS)
Banks, H. T.; Holm, K.; Kappel, F.
2011-07-01
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).
Spectral finite-element methods for parametric constrained optimization problems.
Anitescu, M.; Mathematics and Computer Science
2009-01-01
We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter problem is solvable because it is feasible for a sufficiently large degree of the polynomial approximation and has an objective function with bounded level sets. In addition, the solutions of the finite-dimensional problems converge for an increasing degree of the polynomials considered, provided that the solutions exhibit a sufficiently large and uniform degree of smoothness. Our approach solves, in the case of optimization problems with uncertain parameters, the most computationally intensive part of stochastic finite-element approaches. We demonstrate that our framework is applicable to parametric eigenvalue problems.
Pathwise Coordinate optimization
Friedman, Jerome Isaac; Hoefling, Holger; Tibshirani, Robert
2007-01-01
We consider ``one-at-a-time'' coordinate-wise descent algorithms for a class of convex optimization problems. An algorithm of this kind has been proposed for the L_1-penalized regression (lasso) in the lterature, but it seems to hav e been largely ignored. Indeed, it seems that coordinate-wise algorithms are not often used in convex optimization. We show that this algorithm is very competitive with the well known LARS (or hom otopy) procedure in large lasso problems, and that it can be applied to related methods such as t he garotte and elastic net. It turns out that coordinate-wise descent does not work in the ``fu sed lasso'' however, so we derive a generalized algorithm that yields the solution in much less time that a standard convex optimizer. Finally we generalize the procedure to the two-dimensional fused lasso, and demonstrate its performance on some image smoothing problems.
Group Testing: Four Student Solutions to a Classic Optimization Problem
ERIC Educational Resources Information Center
Teague, Daniel
2006-01-01
This article describes several creative solutions developed by calculus and modeling students to the classic optimization problem of testing in groups to find a small number of individuals who test positive in a large population.
Direct Multiple Shooting Optimization with Variable Problem Parameters
NASA Technical Reports Server (NTRS)
Whitley, Ryan J.; Ocampo, Cesar A.
2009-01-01
Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.
Combinatorial optimization problems with concave costs
Stratila, Dan
2009-01-01
In the first part, we study the problem of minimizing a separable concave function over a polyhedron. We assume the concave functions are nonnegative nondecreasing on R+, and the polyhedron is in RI' (these assumptions can ...
Numerical solution of optimal control problems for complex power systems
NASA Astrophysics Data System (ADS)
Kalimoldayev, Maksat N.; Jenaliyev, Muvasharkhan T.; Abdildayeva, Asel A.; Elezhanova, Shynar K.
2015-09-01
The questions about the decision of optimal control problems for nonlinear system of ordinary differential equations have been considered in this work. In particular, the model considered in this paper describes the controlled processes in electric power systems. Proposed solution methods follow up the principle of expansion of extreme problems based on V.F. Krotov's sufficient conditions of optimality. Numerical experiments shows sufficient efficiency of the used algorithm.
Some Finance Problems Solved with Nonsmooth Optimization Techniques
Vinter, Richard
Some Finance Problems Solved with Nonsmooth Optimization Techniques R. B. VINTER 1 AND H. ZHENG 2 analysis and mathematical finance communities to the scope for applications of nonsmooth optimization to finance, by studying in detail two illustrative examples. The first concerns the maximization of a ter
A Decision Support System for Solving Multiple Criteria Optimization Problems
ERIC Educational Resources Information Center
Filatovas, Ernestas; Kurasova, Olga
2011-01-01
In this paper, multiple criteria optimization has been investigated. A new decision support system (DSS) has been developed for interactive solving of multiple criteria optimization problems (MOPs). The weighted-sum (WS) approach is implemented to solve the MOPs. The MOPs are solved by selecting different weight coefficient values for the criteria…
Strategies for Solving High-Fidelity Aerodynamic Shape Optimization Problems
Papalambros, Panos
Strategies for Solving High-Fidelity Aerodynamic Shape Optimization Problems Zhoujie Lyu Aerodynamic shape optimization based on high-fidelity models is a computational intensive endeavor. The techniques are tested using the Common Research Model wing benchmark defined by the Aerodynamic Design
MATHEMATICAL MODELLING OF SHAPE OPTIMIZATION PROBLEMS FOR SURFACE HARDENING
Henri PoincarÃ© -Nancy-UniversitÃ©, UniversitÃ©
MATHEMATICAL MODELLING OF SHAPE OPTIMIZATION PROBLEMS FOR SURFACE HARDENING DIETMAR H OMBERG #3; AND JAN SOKO LOWSKI y Abstract. We study a mathematical model for induction hardening of steel. An important task for practical applications of induction hardening is to #12;nd the optimal coupling distance
Vision-based stereo ranging as an optimal control problem
NASA Technical Reports Server (NTRS)
Menon, P. K. A.; Sridhar, B.; Chatterji, G. B.
1992-01-01
The recent interest in the use of machine vision for flight vehicle guidance is motivated by the need to automate the nap-of-the-earth flight regime of helicopters. Vision-based stereo ranging problem is cast as an optimal control problem in this paper. A quadratic performance index consisting of the integral of the error between observed image irradiances and those predicted by a Pade approximation of the correspondence hypothesis is then used to define an optimization problem. The necessary conditions for optimality yield a set of linear two-point boundary-value problems. These two-point boundary-value problems are solved in feedback form using a version of the backward sweep method. Application of the ranging algorithm is illustrated using a laboratory image pair.
NASA Astrophysics Data System (ADS)
Briceño-Arias, Luis M.; Hoang, Nguyen Dinh; Peypouquet, Juan
2016-01-01
We study optimal control problems governed by maximal monotone differential inclusions with mixed control-state constraints in infinite dimensional spaces. We obtain some existence results for this kind of dynamics and construct the discrete approximations that allows us to strongly approximate optimal solutions of the continuous-type optimal control problems by their discrete counterparts. Our approach allows us to apply our results for a wide class of mappings that are applicable in mechanics and material sciences.
OPTIMIZATION TECHNIQUES FOR SOLVING BASIS PURSUIT PROBLEMS
Sivaramakrishnan, Kartik K.
. MATLAB code for minimizing the 1-norm of x . . . . . . . . . . . . . . . . 22 B. MATLAB code for minimizing the 2-norm of x . . . . . . . . . . . . . . . . 24 iii #12;C. MATLAB codes for solving data . . . . . . . . . . . . . . . . . . . . . . . . 28 D. MATLAB codes for solving signal denoising problems using BP . . . . . . 29 iv #12;LIST
Cooperative optimal path planning for herding problems
Lu, Zhenyu
2009-05-15
] method has been widely used in military applications such as aerial intercept guided missile systems [7]. In most of the pursuit evasion models considered to date, the pursuer?s aim is to intercept or hunt the evader. Very natural and interesting...) try to control the motion of another group (the ock). It mainly focuses on group behavior instead of the optimal path for the ock to travel to the goal. The journal model is IEEE Transactions on Automatic Control. 2 Multiple robot systems have been a...
The Proportional Colouring Problem: Optimizing Buffers in Wireless Mesh Networks
Bermond, Jean-Claude
Abstract In this paper, we consider a new edge colouring problem motivated by wireless mesh networks optimization: the proportional edge colouring problem. Given a graph G with positive weights associated to its edges, we want to find a proper edge colouring which assigns to each edge at least a proportion (given
Ant Colony Optimization for Multiple Knapsack Problem and Heuristic Model
Fidanova, Stefka
solutions. Modern heuristics include simulated annealing [7], genetic algorithms [4], tabu search [5], antAnt Colony Optimization for Multiple Knapsack Problem and Heuristic Model Stefka Fidanova (stefka practical problems from di#11;erent domains, including transport, like cargo loading, cutting stock, bin
Optimization Problems Related to Zigzag Pocket Machining \\Lambda
Arkin, Estie
Optimization Problems Related to Zigzag Pocket Machining \\Lambda Esther M. Arkin (1) y Martin Held (2) z Christopher L. Smith (1) x (1) Department of Applied Mathematics and Statistics State A fundamental problem of manufacturing is to produce mechanical parts from billets by clearing areas within
Contemporary Mathematics Optimal Locations and the Mass Transport Problem
Mou, Libin
mass distributions on Rm of equal total measure. Let c(x, y) be the cost (per unit massContemporary Mathematics Optimal Locations and the Mass Transport Problem Michael McAsey and Libin Mou Abstract. The mass transport problem seeks to find a transport plan to move mass distributed
A New Method for Mapping Optimization Problems onto Neural Networks
Peterson, Carsten
is a reduction of solution space by one dimension by using graded neurons, thereby avoiding the destructive for obtaining approximate solutions to difficult optimization problems within the neural network paradigm. This approach maps the problems onto Potts glass rather than spin glass theories. A systematic prescription
Solving inverse problems of identification type by optimal control methods
Lenhart, S.; Protopopescu, V.; Yong, J.
1997-05-01
Inverse problems of identification type for nonlinear equations are considered within the framework of optimal control theory. The rigorous solution of any particular problem depends on the functional setting, type of equation, and unknown quantity (or quantities) to be determined. Here we present only the general articulations of the formalism. Compared to classical regularization methods (e.g. Tikhonov coupled with optimization schemes), our approach presents several advantages, namely: (i) a systematic procedure to solve inverse problems of identification type; (ii) an explicit expression for the approximations of the solution; and (iii) a convenient numerical solution of these approximations. {copyright} {ital 1997 American Institute of Physics.}
Solving inverse problems of identification type by optimal control methods
Lenhart, S.; Protopopescu, V.; Jiongmin Yong
1997-06-01
Inverse problems of identification type for nonlinear equations are considered within the framework of optimal control theory. The rigorous solution of any particular problem depends on the functional setting, type of equation, and unknown quantity (or quantities) to be determined. Here the authors present only the general articulations of the formalism. Compared to classical regularization methods (e.g. Tikhonov coupled with optimization schemes), their approach presents several advantages, namely: (i) a systematic procedure to solve inverse problems of identification type; (ii) an explicit expression for the approximations of the solution; and (iii) a convenient numerical solution of these approximations.
Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer
Gili Rosenberg; Poya Haghnegahdar; Phil Goddard; Peter Carr; Kesheng Wu; Marcos López de Prado
2015-08-28
We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs (including permanent and temporary market impact), and, significantly, the solution does not require the inversion of a covariance matrix. The discrete multi-period portfolio optimization problem we solve is significantly harder than the continuous variable problem. We present insight into how results may be improved using suitable software enhancements, and why current quantum annealing technology limits the size of problem that can be successfully solved today. The formulation presented is specifically designed to be scalable, with the expectation that as quantum annealing technology improves, larger problems will be solvable using the same techniques.
Romero, Vicente Jose; Ayon, Douglas V.; Chen, Chun-Hung
2003-09-01
A very general and robust approach to solving optimization problems involving probabilistic uncertainty is through the use of Probabilistic Ordinal Optimization. At each step in the optimization problem, improvement is based only on a relative ranking of the probabilistic merits of local design alternatives, rather than on crisp quantification of the alternatives. Thus, we simply ask the question: 'Is that alternative better or worse than this one?' to some level of statistical confidence we require, not: 'HOW MUCH better or worse is that alternative to this one?'. In this paper we illustrate an elementary application of probabilistic ordinal concepts in a 2-D optimization problem. Two uncertain variables contribute to uncertainty in the response function. We use a simple Coordinate Pattern Search non-gradient-based optimizer to step toward the statistical optimum in the design space. We also discuss more sophisticated implementations, and some of the advantages and disadvantages versus non-ordinal approaches for optimization under uncertainty.
OUTPUTSENSITIVE CONSTRUCTION OF CONVEX HULLS TIMOTHY MOONYEW CHAN
Chan, Timothy M.
in computational geometry. This thesis investigates efficient algorithms for the convex hull problem, where Convex Hull Algorithms : : : : : : : : : : : : : : : : : : : : : : 8 1.5 Results in This Thesis for divide and conquer : : : : : : : : : : : : : : : : : : : 36 3.2 A PruneÂandÂDivide Convex Hull Algorithm
Byzantine Convex Consensus: Preliminary Version Lewis Tseng1,3
Vaidya, Nitin
in the convex hull of the input vectors at the fault-free nodes [8, 12]. The d-dimensional vectors can polytope is within the convex hull of the input vectors at the fault-free nodes. We name this problem as Byzantine convex consensus (BCC), and present an asynchronous approximate BCC algorithm with op- timal fault
Salcedo-Sanz, S.; Del Ser, J.; Landa-Torres, I.; Gil-López, S.; Portilla-Figueras, J. A.
2014-01-01
This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems. PMID:25147860
Lessons Learned During Solutions of Multidisciplinary Design Optimization Problems
NASA Technical Reports Server (NTRS)
Patnaik, Suna N.; Coroneos, Rula M.; Hopkins, Dale A.; Lavelle, Thomas M.
2000-01-01
Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. During solution of the multidisciplinary problems several issues were encountered. This paper lists four issues and discusses the strategies adapted for their resolution: (1) The optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. (2) Optimum solutions obtained were infeasible for aircraft and air-breathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. (3) Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. (4) The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through six problems: (1) design of an engine component, (2) synthesis of a subsonic aircraft, (3) operation optimization of a supersonic engine, (4) design of a wave-rotor-topping device, (5) profile optimization of a cantilever beam, and (6) design of a cvlindrical shell. The combined effort of designers and researchers can bring the optimization method from academia to industry.
Sub-problem Optimization With Regression and Neural Network Approximators
NASA Technical Reports Server (NTRS)
Guptill, James D.; Hopkins, Dale A.; Patnaik, Surya N.
2003-01-01
Design optimization of large systems can be attempted through a sub-problem strategy. In this strategy, the original problem is divided into a number of smaller problems that are clustered together to obtain a sequence of sub-problems. Solution to the large problem is attempted iteratively through repeated solutions to the modest sub-problems. This strategy is applicable to structures and to multidisciplinary systems. For structures, clustering the substructures generates the sequence of sub-problems. For a multidisciplinary system, individual disciplines, accounting for coupling, can be considered as sub-problems. A sub-problem, if required, can be further broken down to accommodate sub-disciplines. The sub-problem strategy is being implemented into the NASA design optimization test bed, referred to as "CometBoards." Neural network and regression approximators are employed for reanalysis and sensitivity analysis calculations at the sub-problem level. The strategy has been implemented in sequential as well as parallel computational environments. This strategy, which attempts to alleviate algorithmic and reanalysis deficiencies, has the potential to become a powerful design tool. However, several issues have to be addressed before its full potential can be harnessed. This paper illustrates the strategy and addresses some issues.
Russian Doll Search for solving Constraint Optimization problems
Verfaillie, G.; Lemaitre, M.
1996-12-31
If the Constraint Satisfaction framework has been extended to deal with Constraint Optimization problems, it appears that optimization is far more complex than satisfaction. One of the causes of the inefficiency of complete tree search methods, like Depth First Branch and Bound, lies in the poor quality of the lower bound on the global valuation of a partial assignment, even when using Forward Checking techniques. In this paper, we introduce the Russian Doll Search algorithm which replaces one search by n successive searches on nested subproblems (n being the number of problem variables), records the results of each search and uses them later, when solving larger subproblems, in order to improve the lower bound on the global valuation of any partial assignment. On small random problems and on large real scheduling problems, this algorithm yields surprisingly good results, which greatly improve as the problems get more constrained and the bandwidth of the used variable ordering diminishes.
Integrated network design and scheduling problems : optimization algorithms and applications.
Nurre, Sarah G.; Carlson, Jeffrey J.
2014-01-01
We consider the class of integrated network design and scheduling problems. These problems focus on selecting and scheduling operations that will change the characteristics of a network, while being speci cally concerned with the performance of the network over time. Motivating applications of INDS problems include infrastructure restoration after extreme events and building humanitarian distribution supply chains. While similar models have been proposed, no one has performed an extensive review of INDS problems from their complexity, network and scheduling characteristics, information, and solution methods. We examine INDS problems under a parallel identical machine scheduling environment where the performance of the network is evaluated by solving classic network optimization problems. We classify that all considered INDS problems as NP-Hard and propose a novel heuristic dispatching rule algorithm that selects and schedules sets of arcs based on their interactions in the network. We present computational analysis based on realistic data sets representing the infrastructures of coastal New Hanover County, North Carolina, lower Manhattan, New York, and a realistic arti cial community CLARC County. These tests demonstrate the importance of a dispatching rule to arrive at near-optimal solutions during real-time decision making activities. We extend INDS problems to incorporate release dates which represent the earliest an operation can be performed and exible release dates through the introduction of specialized machine(s) that can perform work to move the release date earlier in time. An online optimization setting is explored where the release date of a component is not known.
Buchanan, Catherine
2008-01-01
The primary focus of this work is a thorough research into the current available techniques for solving nonlinear programming problems. Emphasis is placed on interior-point methods and the connection between optimal ...
Relations between strictly robust optimization problems and a nonlinear scalarization method
NASA Astrophysics Data System (ADS)
Köbis, Elisabeth; Tammer, Christiane
2012-09-01
We study a strictly robust optimization problem in the context of a nonlinear scalarization method. We introduce a strictly robust multicriteria optimization problem and discuss its relation to a well-known scalar strictly robust optimization problem by using the nonlinear scalarization concept. Furthermore, we propose an unrestricted multicriteria optimization problem and note that its set of weakly Pareto optimal solutions contains all solutions of the scalar strictly robust optimization problem.
Convex-relaxed kernel mapping for image segmentation.
Ben Salah, Mohamed; Ben Ayed, Ismail; Jing Yuan; Hong Zhang
2014-03-01
This paper investigates a convex-relaxed kernel mapping formulation of image segmentation. We optimize, under some partition constraints, a functional containing two characteristic terms: 1) a data term, which maps the observation space to a higher (possibly infinite) dimensional feature space via a kernel function, thereby evaluating nonlinear distances between the observations and segments parameters and 2) a total-variation term, which favors smooth segment surfaces (or boundaries). The algorithm iterates two steps: 1) a convex-relaxation optimization with respect to the segments by solving an equivalent constrained problem via the augmented Lagrange multiplier method and 2) a convergent fixed-point optimization with respect to the segments parameters. The proposed algorithm can bear with a variety of image types without the need for complex and application-specific statistical modeling, while having the computational benefits of convex relaxation. Our solution is amenable to parallelized implementations on graphics processing units (GPUs) and extends easily to high dimensions. We evaluated the proposed algorithm with several sets of comprehensive experiments and comparisons, including: 1) computational evaluations over 3D medical-imaging examples and high-resolution large-size color photographs, which demonstrate that a parallelized implementation of the proposed method run on a GPU can bring a significant speed-up and 2) accuracy evaluations against five state-of-the-art methods over the Berkeley color-image database and a multimodel synthetic data set, which demonstrates competitive performances of the algorithm. PMID:24723519
Practical Global Optimization for Multiview Geometry
Kriegman, David J.
Practical Global Optimization for Multiview Geometry Sameer Agarwal1 , Manmohan Krishna Chandraker1@maths.lth.se Abstract. This paper presents a practical method for finding the prov- ably globally optimal solution-convex nature of these problems, this approach provides a theoretical guarantee of global optimality. The for
Practical Global Optimization for Multiview Geometry
Lunds Universitet
Practical Global Optimization for Multiview Geometry Fredrik Kahl1 , Sameer Agarwal2 , Manmohan Abstract This paper presents a practical method for finding the provably globally optimal solution-convex nature of these problems, this approach provides a theoretical guarantee of global optimality
Practical Global Optimization for Multiview Geometry
Zwicker, Matthias
Practical Global Optimization for Multiview Geometry Sameer Agarwal1 , Manmohan Krishna Chandraker1@maths.lth.se Abstract. This paper presents a practical method for finding the provably globally optimal solution-convex nature of these problems, this approach provides a theoretical guarantee of global optimality. The for
Approximating convex Pareto surfaces in multiobjective radiotherapy planning
Craft, David L.; Halabi, Tarek F.; Shih, Helen A.; Bortfeld, Thomas R.
2006-09-15
Radiotherapy planning involves inherent tradeoffs: the primary mission, to treat the tumor with a high, uniform dose, is in conflict with normal tissue sparing. We seek to understand these tradeoffs on a case-to-case basis, by computing for each patient a database of Pareto optimal plans. A treatment plan is Pareto optimal if there does not exist another plan which is better in every measurable dimension. The set of all such plans is called the Pareto optimal surface. This article presents an algorithm for computing well distributed points on the (convex) Pareto optimal surface of a multiobjective programming problem. The algorithm is applied to intensity-modulated radiation therapy inverse planning problems, and results of a prostate case and a skull base case are presented, in three and four dimensions, investigating tradeoffs between tumor coverage and critical organ sparing.
Transformation of Optimal Centralized Controllers Into Near-Global Static Distributed Controllers
Lavaei, Javad
. This condition is then translated into a convex optimization problem. Subse- quently, a regularization term University Abstract--This paper is concerned with the optimal decentral- ized control problem for linear is incorporated into the objective of the proposed optimization problem to indirectly account for the stability
Ant colony optimization for solving university facility layout problem
NASA Astrophysics Data System (ADS)
Mohd Jani, Nurul Hafiza; Mohd Radzi, Nor Haizan; Ngadiman, Mohd Salihin
2013-04-01
Quadratic Assignment Problems (QAP) is classified as the NP hard problem. It has been used to model a lot of problem in several areas such as operational research, combinatorial data analysis and also parallel and distributed computing, optimization problem such as graph portioning and Travel Salesman Problem (TSP). In the literature, researcher use exact algorithm, heuristics algorithm and metaheuristic approaches to solve QAP problem. QAP is largely applied in facility layout problem (FLP). In this paper we used QAP to model university facility layout problem. There are 8 facilities that need to be assigned to 8 locations. Hence we have modeled a QAP problem with n ? 10 and developed an Ant Colony Optimization (ACO) algorithm to solve the university facility layout problem. The objective is to assign n facilities to n locations such that the minimum product of flows and distances is obtained. Flow is the movement from one to another facility, whereas distance is the distance between one locations of a facility to other facilities locations. The objective of the QAP is to obtain minimum total walking (flow) of lecturers from one destination to another (distance).
Problems in the Optimization of Manned Interplanetary Expeditions
NASA Astrophysics Data System (ADS)
Kiforenko, B. N.; Vasil'Ev, I. Yu.
Within the scope of the unified variation problem the authors discuss the optimization of parameters, choosing flight trajectories and optimal flight control as well as control of life support systems in spacecraft in manned interplanetary expeditions. They examine the efficiency of ejecting the life support systems waste by jets from high-thrust rocket engines as compared to partial waste regeneration. They confirm the possibility of manned expeditions to Mars before efficient life support systems based on biological regeneration are developed.
Quadratic Optimization in the Problems of Active Control of Sound
NASA Technical Reports Server (NTRS)
Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).
The expanded LaGrangian system for constrained optimization problems
NASA Technical Reports Server (NTRS)
Poore, A. B.
1986-01-01
Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrainted optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.
The expanded Lagrangian system for constrained optimization problems
NASA Technical Reports Server (NTRS)
Poore, A. B.; Al-Hassan, Q.
1988-01-01
Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrained optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.
Optimality problem of network topology in stocks market analysis
NASA Astrophysics Data System (ADS)
Djauhari, Maman Abdurachman; Gan, Siew Lee
2015-02-01
Since its introduction fifteen years ago, minimal spanning tree has become an indispensible tool in econophysics. It is to filter the important economic information contained in a complex system of financial markets' commodities. Here we show that, in general, that tool is not optimal in terms of topological properties. Consequently, the economic interpretation of the filtered information might be misleading. To overcome that non-optimality problem, a set of criteria and a selection procedure of an optimal minimal spanning tree will be developed. By using New York Stock Exchange data, the advantages of the proposed method will be illustrated in terms of the power-law of degree distribution.
Numerical Solution of Some Types of Fractional Optimal Control Problems
Sweilam, Nasser Hassan; Al-Ajami, Tamer Mostafa; Hoppe, Ronald H. W.
2013-01-01
We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm “optimize first, then discretize” and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Two illustrative examples are included to demonstrate the validity and applicability of the suggested approaches. PMID:24385874
A Discrete Lagrangian Algorithm for Optimal Routing Problems
Kosmas, O. T.; Vlachos, D. S.; Simos, T. E.
2008-11-06
The ideas of discrete Lagrangian methods for conservative systems are exploited for the construction of algorithms applicable in optimal ship routing problems. The algorithm presented here is based on the discretisation of Hamilton's principle of stationary action Lagrangian and specifically on the direct discretization of the Lagrange-Hamilton principle for a conservative system. Since, in contrast to the differential equations, the discrete Euler-Lagrange equations serve as constrains for the optimization of a given cost functional, in the present work we utilize this feature in order to minimize the cost function for optimal ship routing.
Application of clustering global optimization to thin film design problems.
Lemarchand, Fabien
2014-03-10
Refinement techniques usually calculate an optimized local solution, which is strongly dependent on the initial formula used for the thin film design. In the present study, a clustering global optimization method is used which can iteratively change this initial formula, thereby progressing further than in the case of local optimization techniques. A wide panel of local solutions is found using this procedure, resulting in a large range of optical thicknesses. The efficiency of this technique is illustrated by two thin film design problems, in particular an infrared antireflection coating, and a solar-selective absorber coating. PMID:24663856
State-Constrained Optimal Control Problems of Impulsive Differential Equations
Forcadel, Nicolas; Rao Zhiping Zidani, Hasnaa
2013-08-01
The present paper studies an optimal control problem governed by measure driven differential systems and in presence of state constraints. The first result shows that using the graph completion of the measure, the optimal solutions can be obtained by solving a reparametrized control problem of absolutely continuous trajectories but with time-dependent state-constraints. The second result shows that it is possible to characterize the epigraph of the reparametrized value function by a Hamilton-Jacobi equation without assuming any controllability assumption.
A Modified BFGS Formula Using a Trust Region Model for Nonsmooth Convex Minimizations
Cui, Zengru; Yuan, Gonglin; Sheng, Zhou; Liu, Wenjie; Wang, Xiaoliang; Duan, Xiabin
2015-01-01
This paper proposes a modified BFGS formula using a trust region model for solving nonsmooth convex minimizations by using the Moreau-Yosida regularization (smoothing) approach and a new secant equation with a BFGS update formula. Our algorithm uses the function value information and gradient value information to compute the Hessian. The Hessian matrix is updated by the BFGS formula rather than using second-order information of the function, thus decreasing the workload and time involved in the computation. Under suitable conditions, the algorithm converges globally to an optimal solution. Numerical results show that this algorithm can successfully solve nonsmooth unconstrained convex problems. PMID:26501775
Robust Subspace System Identification via Weighted Nuclear Norm Optimization
Seshia, Sanjit A.
Robust Subspace System Identification via Weighted Nuclear Norm Optimization Dorsa Sadigh Henrik, outliers, nuclear norm, sparsity, robust PCA. 1. INTRODUCTION Subspace system identification is a well studied problem in system identification. The problem was recently posed as a convex optimization problem
NASA Astrophysics Data System (ADS)
Liang, Songxin; Liu, Sijia
2014-12-01
Based on the renormalization group method, Kirkinis (2012) [8] obtained an asymptotic solution to Duffing's nonlinear oscillation problem. Kirkinis then asked if the asymptotic solution is optimal. In this paper, an affirmative answer to the open problem is given by means of the homotopy analysis method.
Tractable fitting with convex polynomials via sum-of-squares Alessandro Magnani
. This technique is extended to enforce convexity of f only on a specified region. Also, an algorithm to fit the convex hull of a set of points with a convex sub-level set of a polynomial is presented. This problemTractable fitting with convex polynomials via sum-of-squares Alessandro Magnani Department
PIBEA: Prospect Indicator Based Evolutionary Algorithm for Multiobjective Optimization Problems
Suzuki, Jun
) main- tain sufficient selection pressure, even in high dimensional MOPs, thereby improving convergence velocity toward the Pareto front, and (2) diversify individuals, even in high dimensional MOPs, thereby algo- rithm to solve multiobjective optimization problems (MOPs). In general, an MOP is formally
Optimizing Value and Avoiding Problems in Building Schools.
ERIC Educational Resources Information Center
Brevard County School Board, Cocoa, FL.
This report describes school design and construction delivery processes used by the School Board of Brevard County (Cocoa, Florida) that help optimize value, avoid problems, and eliminate the cost of maintaining a large facility staff. The project phases are examined from project definition through design to construction. Project delivery…
On the adaptive discretization of PDE-based optimization problems
of optimization problems governed by partial differential equations. The finite element Galerkin method provides work with Roland Becker (University of Pau, France), Boris Vexler (RADON Institute, Linz, Austria reduction by checkpointing techniques. In the following, we consider finite element discretization using
Identification problem for a wave equation via optimal control
Lenhart, S.; Liang, M.; Protopopescu, V.
1998-11-01
The authors approximate an identification problem by applying optimal control techniques to a Tikhonov`s regularization. They seek to identify the dispersive coefficient in a wave equation and allow for the case of error or uncertainty in the observations used for the identification.
Two Dimensional Optimal Mechanism Design for a Sequencing Problem
Al Hanbali, Ahmad
University of Twente, Dept. Applied Mathematics, P.O. Box 217, 7500AE Enschede, The Netherlands, {r.p.hoeksma, m.uetz}@utwente.nl Abstract. We propose an optimal mechanism for a sequencing problem where the jobs' processing times and waiting costs are private. Given public priors for jobs' private data, we seek to find
Optimal Website Design with the Constrained Subtree Selection Problem
Adler, Micah
Optimal Website Design with the Constrained Subtree Selection Problem Brent Heeringa1,2 and Micah of websites. Given a hierarchy of topics represented as a DAG G and a probability distribution over the topics design of websites given a set of page topics, weights for the topics, and a hierarchical arrangement
Existence of optimal controls for a free boundary problem
Rathinam, Muruhan
Existence of optimal controls for a free boundary problem Thomas I. Seidman Department) of the interface between a `pure' solid grain and a liquid solution of the same substance with diffusion both. Introduction We take up a `promise' from [4] to consider the controlled evolution (growth
Acuña, Daniel E; Parada, Víctor
2010-01-01
Humans need to solve computationally intractable problems such as visual search, categorization, and simultaneous learning and acting, yet an increasing body of evidence suggests that their solutions to instantiations of these problems are near optimal. Computational complexity advances an explanation to this apparent paradox: (1) only a small portion of instances of such problems are actually hard, and (2) successful heuristics exploit structural properties of the typical instance to selectively improve parts that are likely to be sub-optimal. We hypothesize that these two ideas largely account for the good performance of humans on computationally hard problems. We tested part of this hypothesis by studying the solutions of 28 participants to 28 instances of the Euclidean Traveling Salesman Problem (TSP). Participants were provided feedback on the cost of their solutions and were allowed unlimited solution attempts (trials). We found a significant improvement between the first and last trials and that solutions are significantly different from random tours that follow the convex hull and do not have self-crossings. More importantly, we found that participants modified their current better solutions in such a way that edges belonging to the optimal solution ("good" edges) were significantly more likely to stay than other edges ("bad" edges), a hallmark of structural exploitation. We found, however, that more trials harmed the participants' ability to tell good from bad edges, suggesting that after too many trials the participants "ran out of ideas." In sum, we provide the first demonstration of significant performance improvement on the TSP under repetition and feedback and evidence that human problem-solving may exploit the structure of hard problems paralleling behavior of state-of-the-art heuristics. PMID:20686597
Block-oriented modeling of superstructure optimization problems
Friedman, Z; Ingalls, J; Siirola, JD; Watson, JP
2013-10-15
We present a novel software framework for modeling large-scale engineered systems as mathematical optimization problems. A key motivating feature in such systems is their hierarchical, highly structured topology. Existing mathematical optimization modeling environments do not facilitate the natural expression and manipulation of hierarchically structured systems. Rather, the modeler is forced to "flatten" the system description, hiding structure that may be exploited by solvers, and obfuscating the system that the modeling environment is attempting to represent. To correct this deficiency, we propose a Python-based "block-oriented" modeling approach for representing the discrete components within the system. Our approach is an extension of the Pyomo library for specifying mathematical optimization problems. Through the use of a modeling components library, the block-oriented approach facilitates a clean separation of system superstructure from the details of individual components. This approach also naturally lends itself to expressing design and operational decisions as disjunctive expressions over the component blocks. By expressing a mathematical optimization problem in a block-oriented manner, inherent structure (e.g., multiple scenarios) is preserved for potential exploitation by solvers. In particular, we show that block-structured mathematical optimization problems can be straightforwardly manipulated by decomposition-based multi-scenario algorithmic strategies, specifically in the context of the PySP stochastic programming library. We illustrate our block-oriented modeling approach using a case study drawn from the electricity grid operations domain: unit commitment with transmission switching and N - 1 reliability constraints. Finally, we demonstrate that the overhead associated with block-oriented modeling only minimally increases model instantiation times, and need not adversely impact solver behavior. (C) 2013 Elsevier Ltd. All rights reserved.
Constraint Algorithm for Extremals in Optimal Control Problems
Maria Barbero-Liñan; Miguel C. Muñoz-Lecanda
2008-02-06
A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum Principle. Apart from the design of this general algorithm useful for any optimal control problem, it is showed how it works to split the set of extremals and, in particular, to characterize the strict abnormality. An example of strict abnormal extremal for a particular control-affine system is also given.
Disciplined Convex Programming Michael Grant1, Stephen Boyd1, and Yinyu Ye12
optimization models called disciplined convex programming is introduced. The methodology enforces a setDisciplined Convex Programming Michael Grant1, Stephen Boyd1, and Yinyu Ye12 Department Science and Engineering, Stanford University Summary. A new methodology for constructingconvex
A Convex Geometry-Based Blind Source Separation Method for Separating Nonnegative Sources.
Yang, Zuyuan; Xiang, Yong; Rong, Yue; Xie, Kan
2015-08-01
This paper presents a convex geometry (CG)-based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be column-sum-to-one by mapping the available observation matrix. Then, its zero-samples are found by searching the facets of the convex hull spanned by the mapped observations. Considering these zero-samples, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CG-based method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method. PMID:25203999
Ober-BlÃ¶baum, Sina
Solving Multiobjective Optimal Control Problems in Space Mission Design using Discrete Mechanics numerical methods have been de- veloped to compute trajectories of optimal control problems on the one hand optimal control problems. In this contribution we combine the optimal control method Discrete Mechanics
Lagrange's principle in extremum problems with constraints
NASA Astrophysics Data System (ADS)
Avakov, E. R.; Magaril-Il'yaev, G. G.; Tikhomirov, V. M.
2013-06-01
In this paper a general result concerning Lagrange's principle for so-called smoothly approximately convex problems is proved which encompasses necessary extremum conditions for mathematical and convex programming, the calculus of variations, Lyapunov problems, and optimal control problems with phase constraints. The problem of local controllability for a dynamical system with phase constraints is also considered. In an appendix, results are presented that relate to the development of a 'Lagrangian approach' to problems where regularity is absent and classical approaches are meaningless. Bibliography: 33 titles.
Analysis of a turning point problem in flight trajectory optimization
NASA Technical Reports Server (NTRS)
Gracey, C.
1989-01-01
The optimal control policy for the aeroglide portion of the minimum fuel, orbital plane change problem for maneuvering entry vehicles is reduced to the solution of a turning point problem for the bank angle control. For this problem a turning point occurs at the minimum altitude of the flight, when the flight path angle equals zero. The turning point separates the bank angle control into two outer solutions that are valid away from the turning point. In a neighborhood of the turning point, where the bank angle changes rapidly, an inner solution is developed and matched with the two outer solutions. An asymptotic analysis of the turning point problem is given, and an analytic example is provided to illustrate the construction of the bank angle control.
Optimal least-squares finite element method for elliptic problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Povinelli, Louis A.
1991-01-01
An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.
Fuel-optimal trajectories for aeroassisted coplanar orbital transfer problem
NASA Astrophysics Data System (ADS)
Naidu, Desineni Subbaramaiah; Hibey, Joseph L.; Charalambous, Charalambos D.
1990-03-01
The optimal control problem arising in coplanar orbital transfer employing aeroassist technology is addressed. The maneuver involves the transfer from high to low earth orbit via the atmosphere, with the object of minimizing the total fuel consumption. Simulations are carried out to obtain the fuel-optimal trajectories for flying the spacecraft through the atmosphere. A highlight is the application of an efficient multiple-shooting method for treating the nonlinear two-point boundary value problem resulting from the optimizaion procedure. The strategy for the atmospheric portion of the minimum-fuel transfer is to fly at the maximum lift-to-drag ratio L/D initially in order to recover from the downward plunge, and then to fly at a negative L/D to level off the flight so that the vehicle skips out of the atmosphere with a flight path angle near zero degrees.
Wu, Zong-Sheng; Fu, Wei-Ping; Xue, Ru
2015-01-01
Teaching-learning-based optimization (TLBO) algorithm is proposed in recent years that simulates the teaching-learning phenomenon of a classroom to effectively solve global optimization of multidimensional, linear, and nonlinear problems over continuous spaces. In this paper, an improved teaching-learning-based optimization algorithm is presented, which is called nonlinear inertia weighted teaching-learning-based optimization (NIWTLBO) algorithm. This algorithm introduces a nonlinear inertia weighted factor into the basic TLBO to control the memory rate of learners and uses a dynamic inertia weighted factor to replace the original random number in teacher phase and learner phase. The proposed algorithm is tested on a number of benchmark functions, and its performance comparisons are provided against the basic TLBO and some other well-known optimization algorithms. The experiment results show that the proposed algorithm has a faster convergence rate and better performance than the basic TLBO and some other algorithms as well. PMID:26421005
Asynchronous global optimization techniques for medium and large inversion problems
Pereyra, V.; Koshy, M.; Meza, J.C.
1995-04-01
We discuss global optimization procedures adequate for seismic inversion problems. We explain how to save function evaluations (which may involve large scale ray tracing or other expensive operations) by creating a data base of information on what parts of parameter space have already been inspected. It is also shown how a correct parallel implementation using PVM speeds up the process almost linearly with respect to the number of processors, provided that the function evaluations are expensive enough to offset the communication overhead.
Gaussian optimizers and the additivity problem in quantum information theory
NASA Astrophysics Data System (ADS)
Holevo, A. S.
2015-04-01
This paper surveys two remarkable analytical problems of quantum information theory. The main part is a detailed report on the recent (partial) solution of the quantum Gaussian optimizer problem which establishes an optimal property of Glauber's coherent states -- a particular case of pure quantum Gaussian states. The notion of a quantum Gaussian channel is developed as a non-commutative generalization of an integral operator with Gaussian kernel, and it is shown that the coherent states, and under certain conditions only they, minimize a broad class of concave functionals of the output of a Gaussian channel. Thus, the output states corresponding to a Gaussian input are the `least chaotic', majorizing all the other outputs. The solution, however, is essentially restricted to the gauge-invariant case where a distinguished complex structure plays a special role. Also discussed is the related well-known additivity conjecture, which was solved in principle in the negative some five years ago. This refers to the additivity or multiplicativity (with respect to tensor products of channels) of information quantities related to the classical capacity of a quantum channel, such as the (1\\to p)-norms or the minimal von Neumann or Rényi output entropies. A remarkable corollary of the present solution of the quantum Gaussian optimizer problem is that these additivity properties, while not valid in general, do hold in the important and interesting class of gauge-covariant Gaussian channels. Bibliography: 65 titles.
Solving nonlinear equality constrained multiobjective optimization problems using neural networks.
Mestari, Mohammed; Benzirar, Mohammed; Saber, Nadia; Khouil, Meryem
2015-10-01
This paper develops a neural network architecture and a new processing method for solving in real time, the nonlinear equality constrained multiobjective optimization problem (NECMOP), where several nonlinear objective functions must be optimized in a conflicting situation. In this processing method, the NECMOP is converted to an equivalent scalar optimization problem (SOP). The SOP is then decomposed into several-separable subproblems processable in parallel and in a reasonable time by multiplexing switched capacitor circuits. The approach which we propose makes use of a decomposition-coordination principle that allows nonlinearity to be treated at a local level and where coordination is achieved through the use of Lagrange multipliers. The modularity and the regularity of the neural networks architecture herein proposed make it suitable for very large scale integration implementation. An application to the resolution of a physical problem is given to show that the approach used here possesses some advantages of the point of algorithmic view, and provides processes of resolution often simpler than the usual techniques. PMID:25647664
Guaranteed Discrete Energy Optimization on Large Protein Design Problems.
Simoncini, David; Allouche, David; de Givry, Simon; Delmas, Céline; Barbe, Sophie; Schiex, Thomas
2015-12-01
In Computational Protein Design (CPD), assuming a rigid backbone and amino-acid rotamer library, the problem of finding a sequence with an optimal conformation is NP-hard. In this paper, using Dunbrack's rotamer library and Talaris2014 decomposable energy function, we use an exact deterministic method combining branch and bound, arc consistency, and tree-decomposition to provenly identify the global minimum energy sequence-conformation on full-redesign problems, defining search spaces of size up to 10(234). This is achieved on a single core of a standard computing server, requiring a maximum of 66GB RAM. A variant of the algorithm is able to exhaustively enumerate all sequence-conformations within an energy threshold of the optimum. These proven optimal solutions are then used to evaluate the frequencies and amplitudes, in energy and sequence, at which an existing CPD-dedicated simulated annealing implementation may miss the optimum on these full redesign problems. The probability of finding an optimum drops close to 0 very quickly. In the worst case, despite 1,000 repeats, the annealing algorithm remained more than 1 Rosetta unit away from the optimum, leading to design sequences that could differ from the optimal sequence by more than 30% of their amino acids. PMID:26610100
Issues and Strategies in Solving Multidisciplinary Optimization Problems
NASA Technical Reports Server (NTRS)
Patnaik, Surya
2013-01-01
Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions can be produced by all the three methods. The variation in the weight calculated by the methods was found to be modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.
NASA Technical Reports Server (NTRS)
Tennille, Geoffrey M.; Howser, Lona M.
1993-01-01
The use of the CONVEX computers that are an integral part of the Supercomputing Network Subsystems (SNS) of the Central Scientific Computing Complex of LaRC is briefly described. Features of the CONVEX computers that are significantly different than the CRAY supercomputers are covered, including: FORTRAN, C, architecture of the CONVEX computers, the CONVEX environment, batch job submittal, debugging, performance analysis, utilities unique to CONVEX, and documentation. This revision reflects the addition of the Applications Compiler and X-based debugger, CXdb. The document id intended for all CONVEX users as a ready reference to frequently asked questions and to more detailed information contained with the vendor manuals. It is appropriate for both the novice and the experienced user.
CONVEXIFICATION OF GENERALIZED NETWORK FLOW PROBLEM WITH APPLICATION TO POWER SYSTEMS
Lavaei, Javad
CONVEXIFICATION OF GENERALIZED NETWORK FLOW PROBLEM WITH APPLICATION TO POWER SYSTEMS SOMAYEH to flows may not be unique. A primary application of this work is in optimization over power networks. Recent work on the optimal power flow (OPF) problem has shown that this non-convex problem can be solved
Design and global optimization of high-efficiency thermophotovoltaic
Design and global optimization of high-efficiency thermophotovoltaic systems Peter Bermel,1 function evaluation and global optimization algorithms. Both are applied to two example systems: improved, PhC-based designs present a set of non-convex optimization problems requiring efficient objective
Enhancements on the Convex Programming Based Powered Descent Guidance Algorithm for Mars Landing
NASA Technical Reports Server (NTRS)
Acikmese, Behcet; Blackmore, Lars; Scharf, Daniel P.; Wolf, Aron
2008-01-01
In this paper, we present enhancements on the powered descent guidance algorithm developed for Mars pinpoint landing. The guidance algorithm solves the powered descent minimum fuel trajectory optimization problem via a direct numerical method. Our main contribution is to formulate the trajectory optimization problem, which has nonconvex control constraints, as a finite dimensional convex optimization problem, specifically as a finite dimensional second order cone programming (SOCP) problem. SOCP is a subclass of convex programming, and there are efficient SOCP solvers with deterministic convergence properties. Hence, the resulting guidance algorithm can potentially be implemented onboard a spacecraft for real-time applications. Particularly, this paper discusses the algorithmic improvements obtained by: (i) Using an efficient approach to choose the optimal time-of-flight; (ii) Using a computationally inexpensive way to detect the feasibility/ infeasibility of the problem due to the thrust-to-weight constraint; (iii) Incorporating the rotation rate of the planet into the problem formulation; (iv) Developing additional constraints on the position and velocity to guarantee no-subsurface flight between the time samples of the temporal discretization; (v) Developing a fuel-limited targeting algorithm; (vi) Initial result on developing an onboard table lookup method to obtain almost fuel optimal solutions in real-time.
NASA Astrophysics Data System (ADS)
Gao, Qian
For both the conventional radio frequency and the comparably recent optical wireless communication systems, extensive effort from the academia had been made in improving the network spectrum efficiency and/or reducing the error rate. To achieve these goals, many fundamental challenges such as power efficient constellation design, nonlinear distortion mitigation, channel training design, network scheduling and etc. need to be properly addressed. In this dissertation, novel schemes are proposed accordingly to deal with specific problems falling in category of these challenges. Rigorous proofs and analyses are provided for each of our work to make a fair comparison with the corresponding peer works to clearly demonstrate the advantages. The first part of this dissertation considers a multi-carrier optical wireless system employing intensity modulation (IM) and direct detection (DD). A block-wise constellation design is presented, which treats the DC-bias that conventionally used solely for biasing purpose as an information basis. Our scheme, we term it MSM-JDCM, takes advantage of the compactness of sphere packing in a higher dimensional space, and in turn power efficient constellations are obtained by solving an advanced convex optimization problem. Besides the significant power gains, the MSM-JDCM has many other merits such as being capable of mitigating nonlinear distortion by including a peak-to-power ratio (PAPR) constraint, minimizing inter-symbol-interference (ISI) caused by frequency-selective fading with a novel precoder designed and embedded, and further reducing the bit-error-rate (BER) by combining with an optimized labeling scheme. The second part addresses several optimization problems in a multi-color visible light communication system, including power efficient constellation design, joint pre-equalizer and constellation design, and modeling of different structured channels with cross-talks. Our novel constellation design scheme, termed CSK-Advanced, is compared with the conventional decoupled system with the same spectrum efficiency to demonstrate the power efficiency. Crucial lighting requirements are included as optimization constraints. To control non-linear distortion, the optical peak-to-average-power ratio (PAPR) of LEDs can be individually constrained. With a SVD-based pre-equalizer designed and employed, our scheme can achieve lower BER than counterparts applying zero-forcing (ZF) or linear minimum-mean-squared-error (LMMSE) based post-equalizers. Besides, a binary switching algorithm (BSA) is applied to improve BER performance. The third part looks into a problem of two-phase channel estimation in a relayed wireless network. The channel estimates in every phase are obtained by the linear minimum mean squared error (LMMSE) method. Inaccurate estimate of the relay to destination (RtD) channel in phase 1 could affect estimate of the source to relay (StR) channel in phase 2, which is made erroneous. We first derive a close-form expression for the averaged Bayesian mean-square estimation error (ABMSE) for both phase estimates in terms of the length of source and relay training slots, based on which an iterative searching algorithm is then proposed that optimally allocates training slots to the two phases such that estimation errors are balanced. Analysis shows how the ABMSE of the StD channel estimation varies with the lengths of relay training and source training slots, the relay amplification gain, and the channel prior information respectively. The last part deals with a transmission scheduling problem in a uplink multiple-input-multiple-output (MIMO) wireless network. Code division multiple access (CDMA) is assumed as a multiple access scheme and pseudo-random codes are employed for different users. We consider a heavy traffic scenario, in which each user always has packets to transmit in the scheduled time slots. If the relay is scheduled for transmission together with users, then it operates in a full-duplex mode, where the packets previously collected from users are transmitted to the destination
Lamiraux, Florent
REACTIVE OBSTACLE AVOIDANCE AND TRAJECTORY OPTIMIZATION FOR NONHOLONOMIC SYSTEMS : TWO PROBLEMS in trajectory optimization for complex nonholonomic systems and one in reactive obstacle avoidance for multi avoidance, trajectory optimization 1 INTRODUCTION Path planning for nonholonomic systems has been
An Efficient Optimization Method for Solving Unsupervised Data Classification Problems.
Shabanzadeh, Parvaneh; Yusof, Rubiyah
2015-01-01
Unsupervised data classification (or clustering) analysis is one of the most useful tools and a descriptive task in data mining that seeks to classify homogeneous groups of objects based on similarity and is used in many medical disciplines and various applications. In general, there is no single algorithm that is suitable for all types of data, conditions, and applications. Each algorithm has its own advantages, limitations, and deficiencies. Hence, research for novel and effective approaches for unsupervised data classification is still active. In this paper a heuristic algorithm, Biogeography-Based Optimization (BBO) algorithm, was adapted for data clustering problems by modifying the main operators of BBO algorithm, which is inspired from the natural biogeography distribution of different species. Similar to other population-based algorithms, BBO algorithm starts with an initial population of candidate solutions to an optimization problem and an objective function that is calculated for them. To evaluate the performance of the proposed algorithm assessment was carried on six medical and real life datasets and was compared with eight well known and recent unsupervised data classification algorithms. Numerical results demonstrate that the proposed evolutionary optimization algorithm is efficient for unsupervised data classification. PMID:26336509
An Efficient Optimization Method for Solving Unsupervised Data Classification Problems
Shabanzadeh, Parvaneh; Yusof, Rubiyah
2015-01-01
Unsupervised data classification (or clustering) analysis is one of the most useful tools and a descriptive task in data mining that seeks to classify homogeneous groups of objects based on similarity and is used in many medical disciplines and various applications. In general, there is no single algorithm that is suitable for all types of data, conditions, and applications. Each algorithm has its own advantages, limitations, and deficiencies. Hence, research for novel and effective approaches for unsupervised data classification is still active. In this paper a heuristic algorithm, Biogeography-Based Optimization (BBO) algorithm, was adapted for data clustering problems by modifying the main operators of BBO algorithm, which is inspired from the natural biogeography distribution of different species. Similar to other population-based algorithms, BBO algorithm starts with an initial population of candidate solutions to an optimization problem and an objective function that is calculated for them. To evaluate the performance of the proposed algorithm assessment was carried on six medical and real life datasets and was compared with eight well known and recent unsupervised data classification algorithms. Numerical results demonstrate that the proposed evolutionary optimization algorithm is efficient for unsupervised data classification. PMID:26336509
A Central Difference Numerical Scheme for Fractional Optimal Control Problems
Dumitru Baleanu; Ozlem Defterli; Om P. Agrawal
2008-11-26
This paper presents a modified numerical scheme for a class of Fractional Optimal Control Problems (FOCPs) formulated in Agrawal (2004) where a Fractional Derivative (FD) is defined in the Riemann-Liouville sense. In this scheme, the entire time domain is divided into several sub-domains, and a fractional derivative (FDs) at a time node point is approximated using a modified Gr\\"{u}nwald-Letnikov approach. For the first order derivative, the proposed modified Gr\\"{u}nwald-Letnikov definition leads to a central difference scheme. When the approximations are substituted into the Fractional Optimal Control (FCO) equations, it leads to a set of algebraic equations which are solved using a direct numerical technique. Two examples, one time-invariant and the other time-variant, are considered to study the performance of the numerical scheme. Results show that 1) as the order of the derivative approaches an integer value, these formulations lead to solutions for integer order system, and 2) as the sizes of the sub-domains are reduced, the solutions converge. It is hoped that the present scheme would lead to stable numerical methods for fractional differential equations and optimal control problems.
Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints
Kmet', Tibor; Kmet'ova, Maria
2009-09-09
A feed forward neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The paper extends adaptive critic neural network architecture proposed by [5] to the optimal control problems with control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation method is illustrated by the optimal control problem of nitrogen transformation cycle model. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.
A Stochastic Checkpoint Optimization Problem E. G. Coffman, Jr., Leopold Flatto, Paul E. Wright
Coffman Jr., E. G.
A Stochastic Checkpoint Optimization Problem E. G. Coffman, Jr., Leopold Flatto, Paul E. Wright AT of the distribution F . #12; A Stochastic Checkpoint Optimization Problem E. G. Coffman, Jr., Leopold Flatto, Paul E
Multi-objective evolutionary methods for time-changing portfolio optimization problems
Hatzakis, Iason
2007-01-01
This thesis is focused on the discovery of efficient asset allocations with the use of evolutionary algorithms. The portfolio optimization problem is a multi-objective optimization problem for the conflicting criteria of ...
Optimality conditions for a two-stage reservoir operation problem
NASA Astrophysics Data System (ADS)
Zhao, Jianshi; Cai, Ximing; Wang, Zhongjing
2011-08-01
This paper discusses the optimality conditions for standard operation policy (SOP) and hedging rule (HR) for a two-stage reservoir operation problem using a consistent theoretical framework. The effects of three typical constraints, i.e., mass balance, nonnegative release, and storage constraints under both certain and uncertain conditions are analyzed. When all nonnegative constraints and storage constraints are unbinding, HR results in optimal reservoir operation following the marginal benefit (MB) principle (the MB is equal over current and future stages. However, if any of those constraints are binding, SOP results in the optimal solution, except in some special cases which need to carry over water in the current stage to the future stage, when extreme drought is certain and a higher marginal utility exists for the second stage. Furthermore, uncertainty complicates the effects of the various constraints. A higher uncertainty level in the future makes HR more favorable as water needs to be reserved to defend against the risk caused by uncertainty. Using the derived optimality conditions, an algorithm for solving a numerical model is developed and tested with the Miyun Reservoir in China.
On the robust optimization to the uncertain vaccination strategy problem
NASA Astrophysics Data System (ADS)
Chaerani, D.; Anggriani, N.; Firdaniza
2014-02-01
In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.
On the robust optimization to the uncertain vaccination strategy problem
Chaerani, D. Anggriani, N. Firdaniza
2014-02-21
In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.
Convex bodies of states and maps
Janusz Grabowski; Alberto Ibort; Marek Ku?; Giuseppe Marmo
2013-06-13
We give a general solution to the question when the convex hulls of orbits of quantum states on a finite-dimensional Hilbert space under unitary actions of a compact group have a non-empty interior in the surrounding space of all density states. The same approach can be applied to study convex combinations of quantum channels. The importance of both problems stems from the fact that, usually, only sets with non-vanishing volumes in the embedding spaces of all states or channels are of practical importance. For the group of local transformations on a bipartite system we characterize maximally entangled states by properties of a convex hull of orbits through them. We also compare two partial characteristics of convex bodies in terms of largest balls and maximum volume ellipsoids contained in them and show that, in general, they do not coincide. Separable states, mixed-unitary channels and k-entangled states are also considered as examples of our techniques.
Integrated Planning and Control for Convex-bodied Nonholonomic systems using Local Feedback
Choset, Howie
Integrated Planning and Control for Convex-bodied Nonholonomic systems using Local Feedback Control The problem of simultaneously planning and controlling the motion of a convex-bodied wheeled mobile robot problem for a convex-bodied wheeled mobile robot navigating amongst obstacles. The method uses param
A Convexification Method for a Class of Global Optimization Problems with
Neumaier, Arnold
A Convexification Method for a Class of Global Optimization Problems with ApplicationsÂmail: dli@se.cuhk.edu.hk #12; A CONVEXIFICATION METHOD FOR A CLASS OF GLOBAL OPTIMIZATION PROBLEMS A convexification method is proposed for solving a class of global optimization problems with certain monotone
A Convexification Method for a Class of Global Optimization Problems with
Neumaier, Arnold
A Convexification Method for a Class of Global Optimization Problems with Applications-mail: dli@se.cuhk.edu.hk #12;A CONVEXIFICATION METHOD FOR A CLASS OF GLOBAL OPTIMIZATION PROBLEMS A convexification method is proposed for solving a class of global optimization problems with certain monotone
NASA Astrophysics Data System (ADS)
Izui, K.; Nishiwaki, S.; Yoshimura, M.
2007-12-01
Swarm algorithms such as particle swarm optimization (PSO) are non-gradient probabilistic optimization algorithms that have been successfully applied for global searches in complex problems such as multi-peak problems. However, application of these algorithms to structural and mechanical optimization problems still remains a complex matter since local optimization capability is still inferior to general numerical optimization methods. This article discusses new swarm metaphors that incorporate design sensitivities concerning objective and constraint functions and are applicable to structural and mechanical design optimization problems. Single- and multi-objective optimization techniques using swarm algorithms are combined with a gradient-based method. In the proposed techniques, swarm optimization algorithms and a sequential linear programming (SLP) method are conducted simultaneously. Finally, truss structure design optimization problems are solved by the proposed hybrid method to verify the optimization efficiency.
Analysis of optimal and near-optimal continuous-thrust transfer problems in general circular orbit
NASA Astrophysics Data System (ADS)
Kéchichian, Jean A.
2009-09-01
A pair of practical problems in optimal continuous-thrust transfer in general circular orbit is analyzed within the context of analytic averaging for rapid computations leading to near-optimal solutions. The first problem addresses the minimum-time transfer between inclined circular orbits by proposing an analytic solution based on a split-sequence strategy in which the equatorial inclination and node controls are done separately by optimally selecting the intermediate orbit size at the sequence switch point that results in the minimum-time transfer. The consideration of the equatorial inclination and node state variables besides the orbital velocity variable is needed to further account for the important J2 perturbation that precesses the orbit plane during the transfer, unlike the thrust-only case in which it is sufficient to consider the relative inclination and velocity variables thus reducing the dimensionality of the system equations. Further extensions of the split-sequence strategy with analytic J2 effect are thus possible for equal computational ease. The second problem addresses the maximization of the equatorial inclination in fixed time by adopting a particular thrust-averaging scheme that controls only the inclination and velocity variables, leaving the node at the mercy of the J2 precession, providing robust fast-converging codes that lead to efficient near-optimal solutions. Example transfers for both sets of problems are solved showing near-optimal features as far as transfer time is concerned, by directly comparing the solutions to "exact" purely numerical counterparts that rely on precision integration of the raw unaveraged system dynamics with continuously varying thrust vector orientation in three-dimensional space.
Bayesian nonparametric multivariate convex regression
Hannah, Lauren A
2011-01-01
In many applications, such as economics, operations research and reinforcement learning, one often needs to estimate a multivariate regression function f subject to a convexity constraint. For example, in sequential decision processes the value of a state under optimal subsequent decisions may be known to be convex or concave. We propose a new Bayesian nonparametric multivariate approach based on characterizing the unknown regression function as the max of a random collection of unknown hyperplanes. This specification induces a prior with large support in a Kullback-Leibler sense on the space of convex functions, while also leading to strong posterior consistency. Although we assume that f is defined over R^p, we show that this model has a convergence rate of log(n)^{-1} n^{-1/(d+2)} under the empirical L2 norm when f actually maps a d dimensional linear subspace to R. We design an efficient reversible jump MCMC algorithm for posterior computation and demonstrate the methods through application to value funct...
Convex Optimization Course Welcome Pack
Hall, Julian
PD PD/JH/JG JG/JH/SG/SB MP/JG/SG/SB PR Speakers: SB Â Stephen Boyd (Stanford) PD ÂParesh Date (Brunel) JG Â Jacek Gondzio (Edinburgh) SG Â Sergio GarcÃa Quiles (Edinburgh) JH Â Julian Hall (Edinburgh) MP
Finite element solution of optimal control problems with inequality constraints
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.
1990-01-01
A finite-element method based on a weak Hamiltonian form of the necessary conditions is summarized for optimal control problems. Very crude shape functions (so simple that element numerical quadrature is not necessary) can be used to develop an efficient procedure for obtaining candidate solutions (i.e., those which satisfy all the necessary conditions) even for highly nonlinear problems. An extension of the formulation allowing for discontinuities in the states and derivatives of the states is given. A theory that includes control inequality constraints is fully developed. An advanced launch vehicle (ALV) model is presented. The model involves staging and control constraints, thus demonstrating the full power of the weak formulation to date. Numerical results are presented along with total elapsed computer time required to obtain the results. The speed and accuracy in obtaining the results make this method a strong candidate for a real-time guidance algorithm.
Fast solvers for optimal control problems from pattern formation
NASA Astrophysics Data System (ADS)
Stoll, Martin; Pearson, John W.; Maini, Philip K.
2016-01-01
The modeling of pattern formation in biological systems using various models of reaction-diffusion type has been an active research topic for many years. We here look at a parameter identification (or PDE-constrained optimization) problem where the Schnakenberg and Gierer-Meinhardt equations, two well-known pattern formation models, form the constraints to an objective function. Our main focus is on the efficient solution of the associated nonlinear programming problems via a Lagrange-Newton scheme. In particular we focus on the fast and robust solution of the resulting large linear systems, which are of saddle point form. We illustrate this by considering several two- and three-dimensional setups for both models. Additionally, we discuss an image-driven formulation that allows us to identify parameters of the model to match an observed quantity obtained from an image.
On representation formulas for long run averaging optimal control problem
NASA Astrophysics Data System (ADS)
Buckdahn, R.; Quincampoix, M.; Renault, J.
2015-12-01
We investigate an optimal control problem with an averaging cost. The asymptotic behaviour of the values is a classical problem in ergodic control. To study the long run averaging we consider both Cesàro and Abel means. A main result of the paper says that there is at most one possible accumulation point - in the uniform convergence topology - of the values, when the time horizon of the Cesàro means converges to infinity or the discount factor of the Abel means converges to zero. This unique accumulation point is explicitly described by representation formulas involving probability measures on the state and control spaces. As a byproduct we obtain the existence of a limit value whenever the Cesàro or Abel values are equicontinuous. Our approach allows to generalise several results in ergodic control, and in particular it allows to cope with cases where the limit value is not constant with respect to the initial condition.
Potter, Jerry L.
An Associative Implementation Of Classical Convex Hull Algorithms Maher M. Atwah and Johnnie W for the convex hull problem. These algorithms are a parallel adaptation of the Jarvis March and the Quickhull a set S of points in the plane, the convex hull of S is the smallest convex polygon for which each point
Solving Global Optimization Problems over Polynomials with GloptiPoly 2.1
Henrion, Didier
Solving Global Optimization Problems over Polynomials with GloptiPoly 2.1 Didier Henrion1 to the global optimum. Global optimality is detected and isolated optimal so- lutions are extracted on benchmark test examples from global optimization, combinatorial optimization and polynomial systems
Optimal Design for Parameter Estimation in EEG Problems in a 3D Multilayered Domain
for several different design criteria (D-optimal, SE-optimal, IGSF-optimal). In this present effort, a more in a 3D unit sphere from data on its boundary. In this effort we compare the use of the classical D-optimalOptimal Design for Parameter Estimation in EEG Problems in a 3D Multilayered Domain March 30, 2014
A Probabilistic Convex Hull Query Tool Zhou Zhao, Da Yan and Wilfred Ng
Ng, Wilfred Siu Hung
Terms Algorithms Keywords Probabilistic Convex Hull, Query Processing, Uncertain 1. INTRODUCTION optimization [2]. A large number of algorithms have been proposed to compute convex hull. A- mong them Andrew's Monotone Chain algorithm [6] finds the convex hull of a set of n 2D points in O(n log n) time
Algorithms for bilevel optimization
NASA Technical Reports Server (NTRS)
Alexandrov, Natalia; Dennis, J. E., Jr.
1994-01-01
General multilevel nonlinear optimization problems arise in design of complex systems and can be used as a means of regularization for multi-criteria optimization problems. Here, for clarity in displaying our ideas, we restrict ourselves to general bi-level optimization problems, and we present two solution approaches. Both approaches use a trust-region globalization strategy, and they can be easily extended to handle the general multilevel problem. We make no convexity assumptions, but we do assume that the problem has a nondegenerate feasible set. We consider necessary optimality conditions for the bi-level problem formulations and discuss results that can be extended to obtain multilevel optimization formulations with constraints at each level.
Enhanced ant colony optimization for inventory routing problem
NASA Astrophysics Data System (ADS)
Wong, Lily; Moin, Noor Hasnah
2015-10-01
The inventory routing problem (IRP) integrates and coordinates two important components of supply chain management which are transportation and inventory management. We consider a one-to-many IRP network for a finite planning horizon. The demand for each product is deterministic and time varying as well as a fleet of capacitated homogeneous vehicles, housed at a depot/warehouse, delivers the products from the warehouse to meet the demand specified by the customers in each period. The inventory holding cost is product specific and is incurred at the customer sites. The objective is to determine the amount of inventory and to construct a delivery routing that minimizes both the total transportation and inventory holding cost while ensuring each customer's demand is met over the planning horizon. The problem is formulated as a mixed integer programming problem and is solved using CPLEX 12.4 to get the lower and upper bound (best integer) for each instance considered. We propose an enhanced ant colony optimization (ACO) to solve the problem and the built route is improved by using local search. The computational experiments demonstrating the effectiveness of our approach is presented.
Radio interferometric gain calibration as a complex optimization problem
NASA Astrophysics Data System (ADS)
Smirnov, O. M.; Tasse, C.
2015-05-01
Recent developments in optimization theory have extended some traditional algorithms for least-squares optimization of real-valued functions (Gauss-Newton, Levenberg-Marquardt, etc.) into the domain of complex functions of a complex variable. This employs a formalism called the Wirtinger derivative, and derives a full-complex Jacobian counterpart to the conventional real Jacobian. We apply these developments to the problem of radio interferometric gain calibration, and show how the general complex Jacobian formalism, when combined with conventional optimization approaches, yields a whole new family of calibration algorithms, including those for the polarized and direction-dependent gain regime. We further extend the Wirtinger calculus to an operator-based matrix calculus for describing the polarized calibration regime. Using approximate matrix inversion results in computationally efficient implementations; we show that some recently proposed calibration algorithms such as STEFCAL and peeling can be understood as special cases of this, and place them in the context of the general formalism. Finally, we present an implementation and some applied results of COHJONES, another specialized direction-dependent calibration algorithm derived from the formalism.
Solving Globally-Optimal Threading Problems in ''Polynomial-Time''
Uberbacher, E.C.; Xu, D.; Xu, Y.
1999-04-12
Computational protein threading is a powerful technique for recognizing native-like folds of a protein sequence from a protein fold database. In this paper, we present an improved algorithm (over our previous work) for solving the globally-optimal threading problem, and illustrate how the computational complexity and the fold recognition accuracy of the algorithm change as the cutoff distance for pairwise interactions changes. For a given fold of m residues and M core secondary structures (or simply cores) and a protein sequence of n residues, the algorithm guarantees to find a sequence-fold alignment (threading) that is globally optimal, measured collectively by (1) the singleton match fitness, (2) pairwise interaction preference, and (3) alignment gap penalties, in O(mn + MnN{sup 1.5C-1}) time and O(mn + nN{sup C-1}) space. C, the topological complexity of a fold as we term, is a value which characterizes the overall structure of the considered pairwise interactions in the fold, which are typically determined by a specified cutoff distance between the beta carbon atoms of a pair of amino acids in the fold. C is typically a small positive integer. N represents the maximum number of possible alignments between an individual core of the fold and the protein sequence when its neighboring cores are already aligned, and its value is significantly less than n. When interacting amino acids are required to see each other, C is bounded from above by a small integer no matter how large the cutoff distance is. This indicates that the protein threading problem is polynomial-time solvable if the condition of seeing each other between interacting amino acids is sufficient for accurate fold recognition. A number of extensions have been made to our basic threading algorithm to allow finding a globally-optimal threading under various constraints, which include consistencies with (1) specified secondary structures (both cores and loops), (2) disulfide bonds, (3) active sites, etc.
Hybridizing Particle Filters and Population-based Metaheuristics for Dynamic Optimization Problems
Pantrigo Fernández, Juan José
-reconstruction procedure [15]. On the other hand, many dynamic problems require the estimation of the system stateHybridizing Particle Filters and Population-based Metaheuristics for Dynamic Optimization Problems Many real-world optimization problems are dynamic. These problems require from powerful methods
Learning the Empirical Hardness of Optimization Problems: The case of combinatorial auctions
Shoham, Yoav
Learning the Empirical Hardness of Optimization Problems: The case of combinatorial auctions Kevin for understanding the algorithm-specific empirical hardness of NP-Hard problems. In this work we focus on the empirical hardness of the winner determination problem--an optimization problem arising in combinatorial
Learning the Empirical Hardness of Optimization Problems: The case of combinatorial auctions
Shoham, Yoav
Learning the Empirical Hardness of Optimization Problems: The case of combinatorial auctions Kevin for understanding the algorithmÂspecific empirical hardness of NPÂHard problems. In this work we focus on the empirical hardness of the winner determination problem---an optimization problem arising in combinatorial
Data-based Construction of Convex Region Surrogate (CRS) Models
Grossmann, Ignacio E.
Data-based Construction of Convex Region Surrogate (CRS) Models Qi Zhang, Ignacio E. Grossmann in such optimization frameworks Need to construct computationally tractable but accurate surrogate models, i
An Efficient Algorithm for the Convex Hull of Planar Scattered Point Set
NASA Astrophysics Data System (ADS)
Fu, Z.; Lu, Y.
2012-07-01
Computing the convex hull of a point set is requirement in the GIS applications. This paper studies on the problem of minimum convex hull and presents an improved algorithm for the minimum convex hull of planar scattered point set. It adopts approach that dividing the point set into several sub regions to get an initial convex hull boundary firstly. Then the points on the boundary, which cannot be vertices of the minimum convex hull, are removed one by one. Finally the concave points on the boundary, which cannot be vertices of the minimum convex hull, are withdrew. Experimental analysis shows the efficiency of the algorithm compared with other methods.
Chance-Constrained Guidance With Non-Convex Constraints
NASA Technical Reports Server (NTRS)
Ono, Masahiro
2011-01-01
Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.
Robust semidefinite programming approach to the separability problem
Brandao, Fernando G.S.L.; Vianna, Reinaldo O.
2004-12-01
We express the optimization of entanglement witnesses for arbitrary bipartite states in terms of a class of convex optimization problems known as robust semidefinite programs (RSDPs). We propose, using well known properties of RSDPs, several sufficient tests for separability of mixed states. Our results are then generalized to multipartite density operators.
Human opinion dynamics: An inspiration to solve complex optimization problems
NASA Astrophysics Data System (ADS)
Kaur, Rishemjit; Kumar, Ritesh; Bhondekar, Amol P.; Kapur, Pawan
2013-10-01
Human interactions give rise to the formation of different kinds of opinions in a society. The study of formations and dynamics of opinions has been one of the most important areas in social physics. The opinion dynamics and associated social structure leads to decision making or so called opinion consensus. Opinion formation is a process of collective intelligence evolving from the integrative tendencies of social influence with the disintegrative effects of individualisation, and therefore could be exploited for developing search strategies. Here, we demonstrate that human opinion dynamics can be utilised to solve complex mathematical optimization problems. The results have been compared with a standard algorithm inspired from bird flocking behaviour and the comparison proves the efficacy of the proposed approach in general. Our investigation may open new avenues towards understanding the collective decision making.
Search-space smoothing for combinatorial optimization problems
NASA Astrophysics Data System (ADS)
Schneider, Johannes; Dankesreiter, Markus; Fettes, Werner; Morgenstern, Ingo; Schmid, Martin; Maria Singer, Johannes
1997-02-01
Commonly there are two types of local search approaches known to treat combinatorial optimization problems with very complex search-space structure: One is to introduce very complicated types of local move classes, allowing a bypass of high energetic barriers separating different minima. The second is introducing a control-parameter (i.e. temperature in physics terminology) dependent state space walker, which is - depending on this control parameter - more or less easily able to climb over barriers. A third, less well-known, but very obvious approach is to smooth the search space, i.e. to eliminate barriers between low-energy configurations and therefore to allow a fast and easy approach to the global optimum. This procedure will be discussed in depth in the following work.
Zero Duality Gap in Optimal Power Flow Problem Javad Lavaei and Steven H. Low
Low, Steven H.
-negativity of physical quantities such as resistance and inductance. Index Terms--Power System, Optimal Power Flow power flow (OPF) problem deals with finding an optimal operating point of a power system that mini1 Zero Duality Gap in Optimal Power Flow Problem Javad Lavaei and Steven H. Low Abstract
Globally Optimizing Graph Partitioning Problems Using Message Passing Elad Mezuman Yair Weiss
Globally Optimizing Graph Partitioning Problems Using Message Passing Elad Mezuman Yair Weiss;Globally Optimizing Graph Partitioning Problems Using Message Passing can be found. This makes it difficult whether failures of the algo- rithm are due to failures of the optimization or to the criterion being
Yanikoglu, Berrin
Multiagent Cooperation for Solving Global Optimization Problems: An Extendible Framework of multiagent cooperation for solving global optimization problems through the introduction of a new multiagent of a wide range of global optimization algorithms described as a set of interacting operations. At one
Graph-Theoretic Techniques in D-Optimal Design Problems Kashinath Chatterjee Giri Narasimhan y
Narasimhan, Giri
Graph-Theoretic Techniques in D-Optimal Design Problems Kashinath Chatterjee #3; Giri Narasimhan y February 14, 2001 Abstract We solve several problems in D-Optimal Design theory using techniques from Graph done on D-optimal saturated main-e#11;ect plans (other than those given by orthogonal arrays) when
One-Dimensional Infinite Horizon Nonconcave Optimal Control Problems Arising in Economic Dynamics
Zaslavski, Alexander J.
2011-12-15
We study the existence of optimal solutions for a class of infinite horizon nonconvex autonomous discrete-time optimal control problems. This class contains optimal control problems without discounting arising in economic dynamics which describe a model with a nonconcave utility function.
GloptiPoly: Global Optimization over Polynomials with Matlab and SeDuMi
Henrion, Didier
GloptiPoly: Global Optimization over Polynomials with Matlab and SeDuMi Didier Henrion1,2 , Jean inequality relaxations of the (generally non-convex) global optimization problem of minimizing. It generates a series of lower bounds monotonically converging to the global optimum. Global optimality
Hauck, Cory D; Alldredge, Graham; Tits, Andre
2012-01-01
We present a numerical algorithm to implement entropy-based (M{sub N}) moment models in the context of a simple, linear kinetic equation for particles moving through a material slab. The closure for these models - as is the case for all entropy-based models - is derived through the solution of constrained, convex optimization problem. The algorithm has two components. The first component is a discretization of the moment equations which preserves the set of realizable moments, thereby ensuring that the optimization problem has a solution (in exact arithmetic). The discretization is a second-order kinetic scheme which uses MUSCL-type limiting in space and a strong-stability-preserving, Runge-Kutta time integrator. The second component of the algorithm is a Newton-based solver for the dual optimization problem, which uses an adaptive quadrature to evaluate integrals in the dual objective and its derivatives. The accuracy of the numerical solution to the dual problem plays a key role in the time step restriction for the kinetic scheme. We study in detail the difficulties in the dual problem that arise near the boundary of realizable moments, where quadrature formulas are less reliable and the Hessian of the dual objection function is highly ill-conditioned. Extensive numerical experiments are performed to illustrate these difficulties. In cases where the dual problem becomes 'too difficult' to solve numerically, we propose a regularization technique to artificially move moments away from the realizable boundary in a way that still preserves local particle concentrations. We present results of numerical simulations for two challenging test problems in order to quantify the characteristics of the optimization solver and to investigate when and how frequently the regularization is needed.
Convex Onion Peeling Genetic Algorithm: An Efficient Solution to Map Labeling of Point-Feature
Bae, Wan
Convex Onion Peeling Genetic Algorithm: An Efficient Solution to Map Labeling of Point-Feature Wan-feature and develop a new genetic algorithm to solve this problem. We adopt a data struc- ture called convex onion peeling and utilize it in our pro- posed Convex Onion Peeling Genetic Algorithm (COPGA) to efficiently
AN ASSOCIATIVE DYNAMIC CONVEX HULL MAHER M. ATWAH JOHNNIE W. BAKER
Potter, Jerry L.
AN ASSOCIATIVE DYNAMIC CONVEX HULL ALGORITHM MAHER M. ATWAH JOHNNIE W. BAKER Mathematics a new parallel algorithm for the dynamic convex hull problem. This algorithm is a parallel adaptation The convex hull of a nite set of a set S of n planar points is an important geometric concept. It can be de
Computing the convex hull of disks using only their chirotope Luc Habert and Michel Pocchiola
Pocchiola, Michel
been developped to design output sensitive convex hull algorithm [4]. (The reÂ lated problemÂ gorithm that computes a pseudoÂtriangulation given the convexÂhull. This algorithm also runs in O(n log n algorithms, and our algorithms use simpler dataÂstructures. Theoretical motivations The convex hull deÂ pends
JOURNAL OF ALGORITHMS 14, 381-394 (1993) Convex Hulls for Random Lines
Devroye, Luc
1993-01-01
JOURNAL OF ALGORITHMS 14, 381-394 (1993) Convex Hulls for Random Lines Luc DEVROYE AND GODFRIED an 0(n log n) time algorithm for computing such a convex hull . Let NI, and N,1 be the number of points-case time algorithm with 0(n) space for this problem. They show that the vertices of the convex hull of I
Computing Optimal Experimental Designs via Interior Point Zhaosong Lu
Lu, Zhaosong
Computing Optimal Experimental Designs via Interior Point Method Zhaosong Lu Ting Kei Pong design, A-criterion, c-criterion, D-criterion, pth mean criterion, interior point method 1 Introduction experimental design problems with a broad class of smooth convex optimality criteria, including the classical A
Network Topologies Guaranteeing Zero Duality Gap for Optimal Power Flow Problem
Lavaei, Javad
power flow (OPF) problem is concerned with finding an optimal operating point of a power system, which relaxation for the load flow problem of a radial distribution system. The generalization of this result1 Network Topologies Guaranteeing Zero Duality Gap for Optimal Power Flow Problem Somayeh Sojoudi
Finite Element Solution of Optimal Control Problems Arising in Semiconductor Modeling
Siefert, Chris
Finite Element Solution of Optimal Control Problems Arising in Semiconductor Modeling Pavel Bochev, and inverse problems arising in the modeling of semiconductor devices lead to optimization problems Introduction Common objectives in the modeling of semiconductor devices are, e.g., to control the current flow
Luo Yousong
2010-06-15
In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary and a functional of the control together with the solution of the state equation under such a control will be minimized. A constraint on the solution of the state equation is also considered.
Generalized vector calculus on convex domain
NASA Astrophysics Data System (ADS)
Agrawal, Om P.; Xu, Yufeng
2015-06-01
In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.
A Convex Approach to Fault Tolerant Control
NASA Technical Reports Server (NTRS)
Maghami, Peiman G.; Cox, David E.; Bauer, Frank (Technical Monitor)
2002-01-01
The design of control laws for dynamic systems with the potential for actuator failures is considered in this work. The use of Linear Matrix Inequalities allows more freedom in controller design criteria than typically available with robust control. This work proposes an extension of fault-scheduled control design techniques that can find a fixed controller with provable performance over a set of plants. Through convexity of the objective function, performance bounds on this set of plants implies performance bounds on a range of systems defined by a convex hull. This is used to incorporate performance bounds for a variety of soft and hard failures into the control design problem.
Advancement and analysis of Gauss pseudospectral transcription for optimal control problems
Huntington, Geoffrey Todd, 1979-
2007-01-01
As optimal control problems become increasingly complex, innovative numerical methods are needed to solve them. Direct transcription methods, and in particular, methods involving orthogonal collocation have become quite ...
NASA Astrophysics Data System (ADS)
Swaidan, Waleeda; Hussin, Amran
2015-10-01
Most direct methods solve finite time horizon optimal control problems with nonlinear programming solver. In this paper, we propose a numerical method for solving nonlinear optimal control problem with state and control inequality constraints. This method used quasilinearization technique and Haar wavelet operational matrix to convert the nonlinear optimal control problem into a quadratic programming problem. The linear inequality constraints for trajectories variables are converted to quadratic programming constraint by using Haar wavelet collocation method. The proposed method has been applied to solve Optimal Control of Multi-Item Inventory Model. The accuracy of the states, controls and cost can be improved by increasing the Haar wavelet resolution.
Perevalov, Eugene
2013-01-01
When additional information sources are available in decision making problems that allow stochastic optimization formulations, an important question is how to optimally use the information the sources are capable of providing. A framework that relates information accuracy determined by the source's knowledge structure to its relevance determined by the problem being solved was proposed in a companion paper. There, the problem of optimal information acquisition was formulated as that of minimization of the expected loss of the solution subject to constraints dictated by the information source knowledge structure and depth. Approximate solution methods for this problem are developed making use of probability metrics method and its application for scenario reduction in stochastic optimization.
Finite element approximation of an optimal control problem for the von Karman equations
NASA Technical Reports Server (NTRS)
Hou, L. Steven; Turner, James C.
1994-01-01
This paper is concerned with optimal control problems for the von Karman equations with distributed controls. We first show that optimal solutions exist. We then show that Lagrange multipliers may be used to enforce the constraints and derive an optimality system from which optimal states and controls may be deduced. Finally we define finite element approximations of solutions for the optimality system and derive error estimates for the approximations.
New approach for the solution of optimal control problems on parallel machines. Doctoral thesis
Stech, D.J.
1990-01-01
This thesis develops a highly parallel solution method for nonlinear optimal control problems. Balakrishnan's epsilon method is used in conjunction with the Rayleigh-Ritz method to convert the dynamic optimization of the optimal control problem into a static optimization problem. Walsh functions and orthogonal polynomials are used as basis functions to implement the Rayleigh-Ritz method. The resulting static optimization problem is solved using matrix operations which have well defined massively parallel solution methods. To demonstrate the method, a variety of nonlinear optimal control problems are solved. The nonlinear Raleigh problem with quadratic cost and nonlinear van der Pol problem with quadratic cost and terminal constraints on the states are solved in both serial and parallel on an eight processor Intel Hypercube. The solutions using both Walsh functions and Legendre polynomials as basis functions are given. In addition to these problems which are solved in parallel, a more complex nonlinear minimum time optimal control problem and nonlinear optimal control problem with an inequality constraint on the control are solved. Results show the method converges quickly, even from relatively poor initial guesses for the nominal trajectories.
NASA Astrophysics Data System (ADS)
Schütze, Niels; Wöhling, Thomas; de Play, Michael
2010-05-01
Some real-world optimization problems in water resources have a high-dimensional space of decision variables and more than one objective function. In this work, we compare three general-purpose, multi-objective simulation optimization algorithms, namely NSGA-II, AMALGAM, and CMA-ES-MO when solving three real case Multi-objective Optimization Problems (MOPs): (i) a high-dimensional soil hydraulic parameter estimation problem; (ii) a multipurpose multi-reservoir operation problem; and (iii) a scheduling problem in deficit irrigation. We analyze the behaviour of the three algorithms on these test problems considering their formulations ranging from 40 up to 120 decision variables and 2 to 4 objectives. The computational effort required by each algorithm in order to reach the true Pareto front is also analyzed.
Optimal experimental design applied to DC resistivity problems
Coles, Darrell Ardon, 1971-
2008-01-01
The systematic design of experiments to optimally query physical systems through manipulation of the data acquisition strategy is termed optimal experimental design (OED). This dissertation introduces the state-of-the-art ...
Aircraft Routing -A Global Optimization Problem Michael C Bartholomew-Biggs
Neumaier, Arnold
Aircraft Routing - A Global Optimization Problem Michael C Bartholomew-Biggs matqmb@herts.ac.uk University of Hertfordshire, England This paper deals with the problem of calculating aircraft flight paths
Solving Large Scale Optimization Problems by Opposition-Based Differential Evolution (ODE)
Wang, Gaofeng Gary
of the problems is increased from 500D to 1000D. All required details about the testing platform, comparison problems which are difficult to solve for the classical optimization methods. Tackling problems with mixed, for many real-world applications, we are faced with problems which contain a huge num- ber of variables
Mascarenhas, Walter Figueiredo
Convex hull, simple polygon, analysis of algorithms 1. Introduction The problem of determining the convex THE CONVEX HULL OF A SIhIPLE POLYGON * Duncan McCALLUM and David AVIS School of Computer Science, Mc was supported by the National Research Council of Canada under research grant NRC A3013. The convex hull
A Cascade Optimization Strategy for Solution of Difficult Multidisciplinary Design Problems
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.; Berke, Laszlo
1996-01-01
A research project to comparatively evaluate 10 nonlinear optimization algorithms was recently completed. A conclusion was that no single optimizer could successfully solve all 40 problems in the test bed, even though most optimizers successfully solved at least one-third of the problems. We realized that improved search directions and step lengths, available in the 10 optimizers compared, were not likely to alleviate the convergence difficulties. For the solution of those difficult problems we have devised an alternative approach called cascade optimization strategy. The cascade strategy uses several optimizers, one followed by another in a specified sequence, to solve a problem. A pseudorandom scheme perturbs design variables between the optimizers. The cascade strategy has been tested successfully in the design of supersonic and subsonic aircraft configurations and air-breathing engines for high-speed civil transport applications. These problems could not be successfully solved by an individual optimizer. The cascade optimization strategy, however, generated feasible optimum solutions for both aircraft and engine problems. This paper presents the cascade strategy and solutions to a number of these problems.
--Convexity, financial transmission rights (FTRs), optimization methods, power flow analysis, power system economics. I1790 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 4, NOVEMBER 2005 Convexity of the Set. INTRODUCTION THE ISSUE OF convexity of power flow solutions arises on occasion, particularly in relation
Wang, Gaofeng Gary
1 Adaptive Response Surface Method A Global Optimization Scheme for Approximation-based Design function evaluations. Extensive tests on the ARSM as a global optimization scheme using benchmark problems of the approach are also discussed. Keywords : Response Surface Method, Approximate Optimization, Global
Collocation and inversion for a reentry optimal control problem Tobias NECKEL 1
trajectory optimization as an enabling technology for versatile real-time trajectory gen- eration efficient trajectory optimization as an enabling technology for versatile real-time trajectory generationCollocation and inversion for a reentry optimal control problem Tobias NECKEL 1 Christophe TALBOT 2
Bobrow, James E.
A Fast Sequential Linear Quadratic Algorithm for Solving Unconstrained Nonlinear Optimal Control a quadratic performance measure. We formulate the optimal control problem in discrete-time, but many-known necessary conditions for the optimal control. We also show that the algorithm is a Gauss-Newton method
inv lvea journal of mathematics Discrete time optimal control applied to pest control problems
Ding, Wandi
inv lvea journal of mathematics msp Discrete time optimal control applied to pest control problems INVOLVE 7:4 (2014) dx.doi.org/10.2140/involve.2014.7.479 Discrete time optimal control applied to pest (Communicated by Suzanne Lenhart) We apply discrete time optimal control theory to the mathematical modeling
Ryan Babbush; Vasil Denchev; Nan Ding; Sergei Isakov; Hartmut Neven
2014-06-17
Quantum annealing is a heuristic quantum algorithm which exploits quantum resources to minimize an objective function embedded as the energy levels of a programmable physical system. To take advantage of a potential quantum advantage, one needs to be able to map the problem of interest to the native hardware with reasonably low overhead. Because experimental considerations constrain our objective function to take the form of a low degree PUBO (polynomial unconstrained binary optimization), we employ non-convex loss functions which are polynomial functions of the margin. We show that these loss functions are robust to label noise and provide a clear advantage over convex methods. These loss functions may also be useful for classical approaches as they compile to regularized risk expressions which can be evaluated in constant time with respect to the number of training examples.
Correlation structure of landscapes of NP-complete optimization problems at finite temperatures
Salamon, Peter
Correlation structure of landscapes of NP-complete optimization problems at finite temperatures of energy values sampled in the energy landscapes of four different combinatorial optimization problems are described in terms of energy landscapes [1]. Technically, we de- fine a landscape to be a (large but finite
Ledzewicz, Urszula
Chemotherapy* Heinz Sch¨attler Dept. of Electrical and Systems Engineering, Washington University, St. Louis of cancer cells under combination chemotherapies are considered as multi-input optimal control problems over for chemotherapy over a fixed therapy interval. For these problems, and consistent with medical practice, optimal
A Honey-bee Mating Optimization Algorithm for Educational Timetabling Problems
Qu, Rong
1 A Honey-bee Mating Optimization Algorithm for Educational Timetabling Problems Nasser R. Sabar1 of the Honey-bee Mating Optimization Algorithm for solv- ing educational timetabling problems. The honey-bee algorithm is a nature inspired algorithm which sim- ulates the process of real honey-bees mating
Solving Continuous-Time Optimal-Control Problems with a Spreadsheet.
ERIC Educational Resources Information Center
Naevdal, Eric
2003-01-01
Explains how optimal control problems can be solved with a spreadsheet, such as Microsoft Excel. Suggests the method can be used by students, teachers, and researchers as a tool to find numerical solutions for optimal control problems. Provides several examples that range from simple to advanced. (JEH)
20.18 Optimization Problems in Air Pollution Modeling Ivan Dimov, and Zahari Zlatev
Dimov, Ivan
20.18 Optimization Problems in Air Pollution Modeling Ivan Dimov, and Zahari Zlatev ABSTRACT. The appearance of optimization problems in the field of air pollution modeling and their importance arising in air pollution modeling will be considered. We shall present a review of some approaches
Geometric optimal control of the contrast imaging problem in Nuclear Magnetic Resonance
B. Bonnard; O. Cots; S. J. Glaser; M. Lapert; D. Sugny; Y. Zhang
2012-08-14
The objective of this article is to introduce the tools to analyze the contrast imaging problem in Nuclear Magnetic Resonance. Optimal trajectories can be selected among extremal solutions of the Pontryagin Maximum Principle applied to this Mayer type optimal problem. Such trajectories are associated to the question of extremizing the transfer time. Hence the optimal problem is reduced to the analysis of the Hamiltonian dynamics related to singular extremals and their optimality status. This is illustrated by using the examples of cerebrospinal fluid / water and grey / white matter of cerebrum.
DC optimization modeling for shape-based recognition
NASA Astrophysics Data System (ADS)
Sturtz, Kirk; Arnold, Gregory; Ferrara, Matthew
2009-05-01
This paper addresses several fundamental problems that have hindered the development of model-based recognition systems: (a) The feature-correspondence problem whose complexity grows exponentially with the number of image points versus model points, (b) The restriction of matching image data points to a point-based model (e.g., point based features), and (c) The local versus global minima issue associated with using an optimization model. Using a convex hull representation for the surfaces of an object, common in CAD models, allows generalizing the point-to-point matching problem to a point-to-surface matching problem. A discretization of the Euclidean transformation variables and use of the well known assignment model of Linear Programming renown leads to a multilinear programming problem. Using a logarithmic/exponential transformation employed in geometric programming this nonconvex optimization problem can be transformed into a difference of convex functions (DC) optimization problem which can be solved using a DC programming algorithm.
Optimal design for parameter estimation in EEG problems in a 3D multilayered domain.
Banks, H T; Rubio, D; Saintier, N; Troparevsky, M I
2015-08-01
The fundamental problem of collecting data in the ``best way'' in order to assure statistically efficient estimation of parameters is known as Optimal Experimental Design. Many inverse problems consist in selecting best parameter values of a given mathematical model based on fits to measured data. These are usually formulated as optimization problems and the accuracy of their solutions depends not only on the chosen optimization scheme but also on the given data. We consider an electromagnetic interrogation problem, specifically one arising in an electroencephalography (EEG) problem, of finding optimal number and locations for sensors for source identification in a 3D unit sphere from data on its boundary. In this effort we compare the use of the classical D-optimal criterion for observation points as opposed to that for a uniform observation mesh. We consider location and best number of sensors and report results based on statistical uncertainty analysis of the resulting estimated parameters. PMID:25974344
Delfim F. M. Torres
2004-11-08
We obtain a version of Noether's invariance theorem for optimal control problems with a finite number of cost functionals. The result is obtained by formulating E. Noether's result to optimal control problems subject to isoperimetric constraints, and then using the unimprovable (Pareto) notion of optimality. A result of this kind was posed to the author, as a mathematical open question, of great interest in applications of control engineering, by A. Gugushvili.
Optimal Conditions for the Control Problem Associated to a Biomedical Process
NASA Astrophysics Data System (ADS)
Bund?u, O.; Juratoni, A.; Chevere?an, A.
2010-09-01
This paper considers a mathematical model of infectious disease of SIS type. We will analyze the problem of minimizing the cost of diseases trough medical treatment. Mathematical modeling of this process leads to an optimal control problem with a finite horizon. The necessary conditions for optimality are given. Using the optimality conditions we prove the existence, uniqueness and stability of the steady state for a differential equations system.
Finite-horizon optimal investment with transaction costs: A parabolic double obstacle problem
NASA Astrophysics Data System (ADS)
Dai, Min; Yi, Fahuai
This paper concerns optimal investment problem of a CRRA investor who faces proportional transaction costs and finite time horizon. From the angle of stochastic control, it is a singular control problem, whose value function is governed by a time-dependent HJB equation with gradient constraints. We reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. This enables us to make use of the well-developed theory of obstacle problem to attack the problem. The C regularity of the value function is proven and the behaviors of the free boundaries are completely characterized.
Interior Point Methods for Computing Optimal Designs
Lu, Zhaosong
2010-01-01
In this paper we study interior point (IP) methods for solving optimal design problems. In particular, we propose a primal IP method for solving the problems with general convex optimality criteria and establish its global convergence. In addition, we reformulate the problems with A-, D- and E-criterion into linear or log-determinant semidefinite programs (SDPs) and apply standard primal-dual IP solvers such as SDPT3 [21,25] to solve the resulting SDPs. We also compare the IP methods with the widely used multiplicative algorithm introduced by Silvey et al. [18]. The computational results show that the IP methods generally outperform the multiplicative algorithm both in speed and solution quality. Moreover, our primal IP method theoretically converges for general convex optimal design problems while the multiplicative algorithm is only known to converge under some assumptions.
Cano, Emilio L.; Moguerza, Javier M.; Alonso-Ayuso, Antonio
2015-01-01
Optimization instances relate to the input and output data stemming from optimization problems in general. Typically, an optimization problem consists of an objective function to be optimized (either minimized or maximized) and a set of constraints. Thus, objective and constraints are jointly a set of equations in the optimization model. Such equations are a combination of decision variables and known parameters, which are usually related to a set domain. When this combination is a linear combination, we are facing a classical Linear Programming (LP) problem. An optimization instance is related to an optimization model. We refer to that model as the Symbolic Model Specification (SMS) containing all the sets, variables, and parameters symbols and relations. Thus, a whole instance is composed by the SMS, the elements in each set, the data values for all the parameters, and, eventually, the optimal decisions resulting from the optimization solution. This data article contains several optimization instances from a real-world optimization problem relating to investment planning on energy efficient technologies at the building level.
Computational and statistical tradeoffs via convex relaxation
Chandrasekaran, Venkat; Jordan, Michael I.
2013-01-01
Modern massive datasets create a fundamental problem at the intersection of the computational and statistical sciences: how to provide guarantees on the quality of statistical inference given bounds on computational resources, such as time or space. Our approach to this problem is to define a notion of “algorithmic weakening,” in which a hierarchy of algorithms is ordered by both computational efficiency and statistical efficiency, allowing the growing strength of the data at scale to be traded off against the need for sophisticated processing. We illustrate this approach in the setting of denoising problems, using convex relaxation as the core inferential tool. Hierarchies of convex relaxations have been widely used in theoretical computer science to yield tractable approximation algorithms to many computationally intractable tasks. In the current paper, we show how to endow such hierarchies with a statistical characterization and thereby obtain concrete tradeoffs relating algorithmic runtime to amount of data. PMID:23479655
A convex complementarity approach for simulating large granular flows.
Tasora, A.; Anitescu, M.; Mathematics and Computer Science; Univ. degli Studi di Parma
2010-07-01
Aiming at the simulation of dense granular flows, we propose and test a numerical method based on successive convex complementarity problems. This approach originates from a multibody description of the granular flow: all the particles are simulated as rigid bodies with arbitrary shapes and frictional contacts. Unlike the discrete element method (DEM), the proposed approach does not require small integration time steps typical of stiff particle interaction; this fact, together with the development of optimized algorithms that can run also on parallel computing architectures, allows an efficient application of the proposed methodology to granular flows with a large number of particles. We present an application to the analysis of the refueling flow in pebble-bed nuclear reactors. Extensive validation of our method against both DEM and physical experiments results indicates that essential collective characteristics of dense granular flow are accurately predicted.
An asymptotically optimal algorithm for pickup and delivery problems
Pavone, Marco
Pickup and delivery problems (PDPs), in which objects or people have to be transported between specific locations, are among the most common combinatorial problems in real-world operations. One particular PDP is the Stacker ...
Application of the method of maximum entropy in the mean to classification problems
NASA Astrophysics Data System (ADS)
Gzyl, Henryk; ter Horst, Enrique; Molina, German
2015-11-01
In this note we propose an application of the method of maximum entropy in the mean to solve a class of inverse problems comprising classification problems and feasibility problems appearing in optimization. Such problems may be thought of as linear inverse problems with convex constraints imposed on the solution as well as on the data. The method of maximum entropy in the mean proves to be a very useful tool to deal with this type of problems.
A global optimization approach to pooling problems in refineries
Pham, Viet
2009-05-15
determining the optimal allocation of intermediate streams to pools and the blending of pools to final products. Because of the presence of bilinear terms, the resulting formulation is nonconvex which makes it very difficult to attain the global solution...
Parallel Multi-Swarm Optimization Framework for Search Problems in Water Distribution Systems
Parallel Multi-Swarm Optimization Framework for Search Problems in Water Distribution Systems Sarat concurrent particle swarms is developed and applied to water distribution problems. Details of the enabling characterization problems for two water distribution networks with 1,834 and 12,457 nodes respectively. 1
Singular optimal control and the identically non-regular problem in the calculus of variations
NASA Technical Reports Server (NTRS)
Menon, P. K. A.; Kelley, H. J.; Cliff, E. M.
1985-01-01
A small but interesting class of optimal control problems featuring a scalar control appearing linearly is equivalent to the class of identically nonregular problems in the Calculus of Variations. It is shown that a condition due to Mancill (1950) is equivalent to the generalized Legendre-Clebsch condition for this narrow class of problems.
Newton's method for large bound-constrained optimization problems.
Lin, C.-J.; More, J. J.; Mathematics and Computer Science
1999-01-01
We analyze a trust region version of Newton's method for bound-constrained problems. Our approach relies on the geometry of the feasible set, not on the particular representation in terms of constraints. The convergence theory holds for linearly constrained problems and yields global and superlinear convergence without assuming either strict complementarity or linear independence of the active constraints. We also show that the convergence theory leads to an efficient implementation for large bound-constrained problems.
Discrete-time entropy formulation of optimal and adaptive control problems
NASA Technical Reports Server (NTRS)
Tsai, Yweting A.; Casiello, Francisco A.; Loparo, Kenneth A.
1992-01-01
The discrete-time version of the entropy formulation of optimal control of problems developed by G. N. Saridis (1988) is discussed. Given a dynamical system, the uncertainty in the selection of the control is characterized by the probability distribution (density) function which maximizes the total entropy. The equivalence between the optimal control problem and the optimal entropy problem is established, and the total entropy is decomposed into a term associated with the certainty equivalent control law, the entropy of estimation, and the so-called equivocation of the active transmission of information from the controller to the estimator. This provides a useful framework for studying the certainty equivalent and adaptive control laws.
Bukhsh, Waqquas Ahmed
2014-07-01
Optimization plays a central role in the control and operation of electricity power networks. In this thesis we focus on two very important optimization problems in power systems. The first is the optimal power flow ...
Initial parameters problem of WNN based on particle swarm optimization
NASA Astrophysics Data System (ADS)
Yang, Chi-I.; Wang, Kaicheng; Chang, Kueifang
2014-04-01
The stock price prediction by the wavelet neural network is about minimizing RMSE by adjusting the parameters of initial values of network, training data percentage, and the threshold value in order to predict the fluctuation of stock price in two weeks. The objective of this dissertation is to reduce the number of parameters to be adjusted for achieving the minimization of RMSE. There are three kinds of parameters of initial value of network: w , t , and d . The optimization of these three parameters will be conducted by the Particle Swarm Optimization method, and comparison will be made with the performance of original program, proving that RMSE can be even less than the one before the optimization. It has also been shown in this dissertation that there is no need for adjusting training data percentage and threshold value for 68% of the stocks when the training data percentage is set at 10% and the threshold value is set at 0.01.
Finite dimensional approximation of a class of constrained nonlinear optimal control problems
NASA Technical Reports Server (NTRS)
Gunzburger, Max D.; Hou, L. S.
1994-01-01
An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.
Solving the optimal attention allocation problem in manual control
NASA Technical Reports Server (NTRS)
Kleinman, D. L.
1976-01-01
Within the context of the optimal control model of human response, analytic expressions for the gradients of closed-loop performance metrics with respect to human operator attention allocation are derived. These derivatives serve as the basis for a gradient algorithm that determines the optimal attention that a human should allocate among several display indicators in a steady-state manual control task. Application of the human modeling techniques are made to study the hover control task for a CH-46 VTOL flight tested by NASA.
NASA Astrophysics Data System (ADS)
Ausaf, Muhammad Farhan; Gao, Liang; Li, Xinyu
2015-10-01
For increasing the overall performance of modern manufacturing systems, effective integration of process planning and scheduling functions has been an important area of consideration among researchers. Owing to the complexity of handling process planning and scheduling simultaneously, most of the research work has been limited to solving the integrated process planning and scheduling (IPPS) problem for a single objective function. As there are many conflicting objectives when dealing with process planning and scheduling, real world problems cannot be fully captured considering only a single objective for optimization. Therefore considering multi-objective IPPS (MOIPPS) problem is inevitable. Unfortunately, only a handful of research papers are available on solving MOIPPS problem. In this paper, an optimization algorithm for solving MOIPPS problem is presented. The proposed algorithm uses a set of dispatching rules coupled with priority assignment to optimize the IPPS problem for various objectives like makespan, total machine load, total tardiness, etc. A fixed sized external archive coupled with a crowding distance mechanism is used to store and maintain the non-dominated solutions. To compare the results with other algorithms, a C-matric based method has been used. Instances from four recent papers have been solved to demonstrate the effectiveness of the proposed algorithm. The experimental results show that the proposed method is an efficient approach for solving the MOIPPS problem.
Some Marginalist Intuition Concerning the Optimal Commodity Tax Problem
ERIC Educational Resources Information Center
Brett, Craig
2006-01-01
The author offers a simple intuition that can be exploited to derive and to help interpret some canonical results in the theory of optimal commodity taxation. He develops and explores the principle that the marginal social welfare loss per last unit of tax revenue generated be equalized across tax instruments. A simple two-consumer,…
Ant Colony Optimization for the Total Weighted Tardiness Problem
Libre de Bruxelles, Université
-1098 SJ Amsterdam, The Netherlands ^ Universite Libre de Bruxelles, IRIDIA, Avenue Franklin Roosevelt] and for which instances with more than 50jobs can often not be solved to optimality with state-of-the-art branch & bound algorithms [1, 5]. In the SMTWTP n jobs have to be sequentially processed on a single machine
Application of Particle Swarm Optimization Algorithm in the Heating System Planning Problem
Ma, Rong-Jiang; Yu, Nan-Yang; Hu, Jun-Yi
2013-01-01
Based on the life cycle cost (LCC) approach, this paper presents an integral mathematical model and particle swarm optimization (PSO) algorithm for the heating system planning (HSP) problem. The proposed mathematical model minimizes the cost of heating system as the objective for a given life cycle time. For the particularity of HSP problem, the general particle swarm optimization algorithm was improved. An actual case study was calculated to check its feasibility in practical use. The results show that the improved particle swarm optimization (IPSO) algorithm can more preferably solve the HSP problem than PSO algorithm. Moreover, the results also present the potential to provide useful information when making decisions in the practical planning process. Therefore, it is believed that if this approach is applied correctly and in combination with other elements, it can become a powerful and effective optimization tool for HSP problem. PMID:23935429
Symmetry of Solutions to the Generalized 1-D Optimal Sojourn Time Control Problem
Zhang, Wei
Symmetry of Solutions to the Generalized 1-D Optimal Sojourn Time Control Problem Wei Zhang the system back to order. Safety of deterministic systems is relatively easy to maintain by properly designed
Structure-exploiting interior point methods for security constrained optimal power flow problems
Chiang, Naiyuan
2013-07-01
The aim of this research is to demonstrate some more efficient approaches to solve the n-1 security constrained optimal power flow (SCOPF) problems by using structure-exploiting primal-dual interior point methods ...
Farhi, Edward
In this paper we study the performance of the quantum adiabatic algorithm on random instances of two combinatorial optimization problems, 3-regular 3-XORSAT and 3-regular max-cut. The cost functions associated with these ...
The solution of singular optimal control problems using direct collocation and nonlinear programming
NASA Astrophysics Data System (ADS)
Downey, James R.; Conway, Bruce A.
1992-08-01
This paper describes work on the determination of optimal rocket trajectories which may include singular arcs. In recent years direct collocation and nonlinear programming has proven to be a powerful method for solving optimal control problems. Difficulties in the application of this method can occur if the problem is singular. Techniques exist for solving singular problems indirectly using the associated adjoint formulation. Unfortunately, the adjoints are not a part of the direct formulation. It is shown how adjoint information can be obtained from the direct method to allow the solution of singular problems.
Optimization technique for problems with an inequality constraint
NASA Technical Reports Server (NTRS)
Russell, K. J.
1972-01-01
General technique uses a modified version of an existing technique termed the pattern search technique. New procedure called the parallel move strategy permits pattern search technique to be used with problems involving a constraint.
Necessary and sufficient conditions under which an H2 optimal control problem has a unique solution
NASA Technical Reports Server (NTRS)
Chen, Ben M.; Saberi, Ali
1993-01-01
A set of necessary and sufficient conditions under which a general H2-optimal control problem has a unique solution is derived. It is shown that the solution for an H2-optimal control problem, if it exists, is unique if and only if (1) the transfer function from the control input to the controlled output is left invertible, and (2) the transfer function from the disturbance to the measurement output is right invertible.
Variational stability of optimal control problems involving subdifferential operators
Tolstonogov, Aleksandr A
2011-04-30
This paper is concerned with the problem of minimizing an integral functional with control-nonconvex integrand over the class of solutions of a control system in a Hilbert space subject to a control constraint given by a phase-dependent multivalued map with closed nonconvex values. The integrand, the subdifferential operators, the perturbation term, the initial conditions and the control constraint all depend on a parameter. Along with this problem, the paper considers the problem of minimizing an integral functional with control-convexified integrand over the class of solutions of the original system, but now subject to a convexified control constraint. By a solution of a control system we mean a 'trajectory-control' pair. For each value of the parameter, the convexified problem is shown to have a solution, which is the limit of a minimizing sequence of the original problem, and the minimal value of the functional with the convexified integrand is a continuous function of the parameter. This property is commonly referred to as the variational stability of a minimization problem. An example of a control parabolic system with hysteresis and diffusion effects is considered. Bibliography: 24 titles.
Decomposition of a Multiobjective Optimization Problem into a Number of Simple Multiobjective
Zhang, Qingfu
an approach for decomposing a multiobjective optimization problem (MOP) into a set of simple multiobjective. In such a way, popula- tion diversity can be maintained, which is critical for solving some MOPs. Experimental with some MOPs. It also explains why MOEA/D-M2M performs better. Keywords-Multiobjective optimization
Male optimality and uniqueness in stable marriage problems with partial orders
Rossi, Francesca
marriages for partially ordered preferences. Male optimality allows us to give priority to one gender overMale optimality and uniqueness in stable marriage problems with partial orders (Extended Abstract of stable marriages for partially ordered prefer- ences. We give an algorithm to find a stable marriage
A Global Optimization Method for the Molecular Replacement Problem in X-ray Crystallography
Zhang, Yin
The primary technique for determining the three-dimensional structure of a protein molecule is X is a global optimization problem to locate an optimal position of a model protein, whose structure is similar to the unknown protein structure that is to be determined, so that at this position the model protein
Kelley, C. T. "Tim"
Application of IFFCO to Optimization of Natural Gas Pipelines 12 4 Hidden Constrants 15 4.1 DefinitionImplicit Filtering for Constrained Optimization and Applications to Problems in the Natural Gas Pipeline Industry 1 Alton Patrick Department of Mathematics Center for Research in Scientific Computation
Qingmeng Wei; Xinling Xiao
2013-12-02
This paper is devoted to the stochastic optimal control problems for systems governed by forward-backward stochastic Volterra integral equations (FBSVIEs, for short) with state constraints. Using Ekeland's variational principle, we obtain one kind of variational inequality. Then, by dual method, we derive a stochastic maximum principle which gives the necessary conditions for the optimal controls.
The Multi-robot Coverage Problem for Optimal Coordinated Search with an Unknown Number of Robots
Minnesota, University of
The Multi-robot Coverage Problem for Optimal Coordinated Search with an Unknown Number of Robots of Minnesota Minneapolis, MN 55455 Email: {hjmin|npapas}@cs.umn.edu Abstract-- This work presents a novel multi-robot coverage scheme for an unknown number of robots; it focuses on optimizing the number of robots and each
Parameterized Approaches for Large-Scale Optimization Problems
Buchanan, Austin Loyd
2015-07-10
Vladimir Boginski, Panos Pardalos, and Oleg Prokopyev have been great to work with, and I thank all of them for writing reference letters for me over the years for scholarships and faculty positions. Dr. Eduardo Pasiliao, my summer mentor at the iv AFRL... Presidential Library Foundation, and the Texas Engineering Founda- tion. My summer research has been supported primarily by the AFRL Mathemati- cal Modeling and Optimization Institute. Partial support by AFOSR under grants FA9550-12-1-0103 and FA8651...
Evaluation of Genetic Algorithm Concepts using Model Problems. Part 1; Single-Objective Optimization
NASA Technical Reports Server (NTRS)
Holst, Terry L.; Pulliam, Thomas H.
2003-01-01
A genetic-algorithm-based optimization approach is described and evaluated using a simple hill-climbing model problem. The model problem utilized herein allows for the broad specification of a large number of search spaces including spaces with an arbitrary number of genes or decision variables and an arbitrary number hills or modes. In the present study, only single objective problems are considered. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all problems attempted. The most difficult problems - those with large hyper-volumes and multi-mode search spaces containing a large number of genes - require a large number of function evaluations for GA convergence, but they always converge.
Multigrid one shot methods for optimal control problems: Infinite dimensional control
NASA Technical Reports Server (NTRS)
Arian, Eyal; Taasan, Shlomo
1994-01-01
The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.
Evaluation of Genetic Algorithm Concepts Using Model Problems. Part 2; Multi-Objective Optimization
NASA Technical Reports Server (NTRS)
Holst, Terry L.; Pulliam, Thomas H.
2003-01-01
A genetic algorithm approach suitable for solving multi-objective optimization problems is described and evaluated using a series of simple model problems. Several new features including a binning selection algorithm and a gene-space transformation procedure are included. The genetic algorithm is suitable for finding pareto optimal solutions in search spaces that are defined by any number of genes and that contain any number of local extrema. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all optimization problems attempted. The binning algorithm generally provides pareto front quality enhancements and moderate convergence efficiency improvements for most of the model problems. The gene-space transformation procedure provides a large convergence efficiency enhancement for problems with non-convoluted pareto fronts and a degradation in efficiency for problems with convoluted pareto fronts. The most difficult problems --multi-mode search spaces with a large number of genes and convoluted pareto fronts-- require a large number of function evaluations for GA convergence, but always converge.
Zatsiorsky, Vladimir M.
2011-01-01
One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423–453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem. PMID:21311907
An Improved Lagrangian Relaxation Method for VLSI Combinational Circuit Optimization
Huang, Yi-Le
2012-02-14
-objectives and proven to reach optimal solution under continuous solution space. However, it is more complex to use Lagrangian relaxation under discrete solution space. The Lagrangian dual problem is non-convex and previously a sub-gradient method was used to solve it...
ERROR ESTIMATES FOR THE FINITE VOLUME ELEMENT METHOD FOR PARABOLIC EQUATIONS IN CONVEX POLYGONAL
Lazarov, Raytcho
ERROR ESTIMATES FOR THE FINITE VOLUME ELEMENT METHOD FOR PARABOLIC EQUATIONS IN CONVEX POLYGONAL piecewise linear finite volume element method for parabolic equations in a convex polygonal domain as in the corresponding finite element method, and almost optimal away from the corners. We also briefly consider
A Convex Speech Extraction Model and Fast Computation by the Split Bregman Method
Ferguson, Thomas S.
1 A Convex Speech Extraction Model and Fast Computation by the Split Bregman Method Meng Yu, Wenye Ma, Jack Xin, and Stanley Osher. Abstract--A fast speech extraction (FSE) method is presented using convex optimization made possible by pause detection of the speech sources. Sparse unmixing filters
A few shape optimization results for a biharmonic Steklov problem
NASA Astrophysics Data System (ADS)
Buoso, Davide; Provenzano, Luigi
2015-09-01
We derive the equation of a free vibrating thin plate whose mass is concentrated at the boundary, namely a Steklov problem for the biharmonic operator. We provide Hadamard-type formulas for the shape derivatives of the corresponding eigenvalues and prove that balls are critical domains under volume constraint. Finally, we prove an isoperimetric inequality for the first positive eigenvalue.
On the Optimal Strategy for an Isotropic Blocking Problem
Bressan, Alberto
no blocking strategy is implemented, the set R(t) is described as the reachable set for a differential) in terms of one single set . = t0 (t) \\ t0 R (t) . (1.3) Given a rectifiable set R2. In connection with this model, two issues naturally arise: Blocking problem: Find an admissible set such that R
Promoting optimal development: screening for behavioral and emotional problems.
Weitzman, Carol; Wegner, Lynn
2015-02-01
By current estimates, at any given time, approximately 11% to 20% of children in the United States have a behavioral or emotional disorder, as defined in the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition. Between 37% and 39% of children will have a behavioral or emotional disorder diagnosed by 16 years of age, regardless of geographic location in the United States. Behavioral and emotional problems and concerns in children and adolescents are not being reliably identified or treated in the US health system. This clinical report focuses on the need to increase behavioral screening and offers potential changes in practice and the health system, as well as the research needed to accomplish this. This report also (1) reviews the prevalence of behavioral and emotional disorders, (2) describes factors affecting the emergence of behavioral and emotional problems, (3) articulates the current state of detection of these problems in pediatric primary care, (4) describes barriers to screening and means to overcome those barriers, and (5) discusses potential changes at a practice and systems level that are needed to facilitate successful behavioral and emotional screening. Highlighted and discussed are the many factors at the level of the pediatric practice, health system, and society contributing to these behavioral and emotional problems. PMID:25624375
Generating optimal Sturmian basis functions for atomic problems
Randazzo, J. M.; Frapiccini, A. L.; Colavecchia, F. D.; Ancarani, L. U.; Gasaneo, G.
2010-04-15
In this paper we discuss the optimization of Sturmian basis functions by studying bound atomic systems within the configuration interaction method. Our investigation clearly shows how the fulfillment of correct physical boundary conditions at short and large distances from the nucleus improves the convergence rate of the method. This is illustrated first through a one-electron atom, and then with the two-electron systems. For the ground state of the helium atom, and with 35 Sturmian functions per electron and angular momenta, we obtain an energy of -2.903 712 820 a.u., outperforming previous similar calculations [Bromley and Mitroy, Int. J. Quantum Chem. 107, 1150 (2007)].
Phan Quoc Khanh Nguyen Dinh Tuan
2008-10-15
First and second-order approximations are used to establish both necessary and sufficient optimality conditions for local weak efficiency and local firm efficiency in nonsmooth set-constrained vector problems. Even continuity and relaxed convexity assumptions are not imposed. Compactness conditions are also relaxed. Examples are provided to show advantages of the presented results over recent existing ones.
New numerical methods for open-loop and feedback solutions to dynamic optimization problems
NASA Astrophysics Data System (ADS)
Ghosh, Pradipto
The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development is that the resulting control law has an algebraic closed-form structure. The proposed method uses an optimal spatial statistical predictor called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. With universal kriging, an approximation to the optimal feedback map is computed by conceptualizing a set of state-control samples from pre-computed extremals to be a particular realization of a jointly Gaussian spatial process. Feedback policies are computed for a variety of example dynamic optimization problems in order to evaluate the effectiveness of this methodology. This feedback synthesis approach is found to combine good numerical accuracy with low computational overhead, making it a suitable candidate for real-time applications. Particle swarm and universal kriging are combined for a capstone example, a near optimal, near-admissible, full-state feedback control law is computed and tested for the heat-load-limited atmospheric-turn guidance of an aeroassisted transfer vehicle. The performance of this explicit guidance scheme is found to be very promising; initial errors in atmospheric entry due to simulated thruster misfirings are found to be accurately corrected while closely respecting the algebraic state-inequality constraint.
Optimal control of a convective boundary condition in a thermistor problem
Hrynkiv, Volodymyr; Lenhart, Suzanne M; Protopopescu, Vladimir A
2008-01-01
We consider the optimal control of a two-dimensional steady-state thermistor. The problem is described by a system of two nonlinear elliptic partial differential equations with appropriate boundary conditions which model the coupling of the thermistor to its surroundings. Based on physical considerations, an objective functional to be minimized is introduced and the convective boundary coefficient is taken as the control. Existence and uniqueness of the optimal control are proven. To characterize this optimal control, the optimality system consisting of the state and adjoint equations is derived.
Tracking and Optimal Control Problems in Human Head/Eye Coordination
Ghosh, Bijoy K.
Tracking and Optimal Control Problems in Human Head/Eye Coordination Indika Wijayasinghe1, Eugenio a dynamic model of the head and eye, the eye movement is modeled as a tracking control problem, where the tracking signal depends on the head movement trajectory. The torques required for the head and eye
A well-posed optimal spectral element approximation for the Stokes problem
NASA Technical Reports Server (NTRS)
Maday, Y.; Patera, A. T.; Ronquist, E. M.
1987-01-01
A method is proposed for the spectral element simulation of incompressible flow. This method constitutes in a well-posed optimal approximation of the steady Stokes problem with no spurious modes in the pressure. The resulting method is analyzed, and numerical results are presented for a model problem.
On Variant Strategies To Solve The Magnitude Least Squares Optimization Problem In Parallel
Weiss, Pierre
1 On Variant Strategies To Solve The Magnitude Least Squares Optimization Problem In Parallel to the magnitude of the spin excitation, and not its phase, the magnitude least squares (MLS) problem-P) methods, semidefinite programming (SDP) and magnitude squared least squares (MSLS) relaxations are studied
The Finite Horizon Optimal Multi-Modes Switching Problem: The Viscosity Solution Approach
El Asri, Brahim Hamadene, Said
2009-10-15
In this paper we show existence and uniqueness of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. This system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is in relation with the valuation of firms in a financial market.
Cameron, Peter
Designs Mutually unbiased bases 2-designs from bases Open problems Optimal complex projective designs Aidan Roy November 6, 2009 #12;Designs Mutually unbiased bases 2-designs from bases Open problems , with equality if and only if X is a t-design. #12;Designs Mutually unbiased bases 2-designs from bases Open
A hybrid symbolic/finite-element algorithm for solving nonlinear optimal control problems
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.
1991-01-01
The general code described is capable of solving difficult nonlinear optimal control problems by using finite elements and a symbolic manipulator. Quick and accurate solutions are obtained with a minimum for user interaction. Since no user programming is required for most problems, there are tremendous savings to be gained in terms of time and money.
LETTER Communicated by Geoffrey Goodhill Exact Solution for the Optimal Neuronal Layout Problem
Chklovskii, Dmitri "Mitya"
LETTER Communicated by Geoffrey Goodhill Exact Solution for the Optimal Neuronal Layout Problem neuronal connectivity, find a spatial layout of neurons that minimizes the wiring cost. Unfortunately, this problem is difficult to solve because the number of possible layouts is often astro- nomically large. We
A distributed approach to the OPF problem
NASA Astrophysics Data System (ADS)
Erseghe, Tomaso
2015-12-01
This paper presents a distributed approach to optimal power flow (OPF) in an electrical network, suitable for application in a future smart grid scenario where access to resource and control is decentralized. The non-convex OPF problem is solved by an augmented Lagrangian method, similar to the widely known ADMM algorithm, with the key distinction that penalty parameters are constantly increased. A (weak) assumption on local solver reliability is required to always ensure convergence. A certificate of convergence to a local optimum is available in the case of bounded penalty parameters. For moderate sized networks (up to 300 nodes, and even in the presence of a severe partition of the network), the approach guarantees a performance very close to the optimum, with an appreciably fast convergence speed. The generality of the approach makes it applicable to any (convex or non-convex) distributed optimization problem in networked form. In the comparison with the literature, mostly focused on convex SDP approximations, the chosen approach guarantees adherence to the reference problem, and it also requires a smaller local computational complexity effort.
An optimal control problem for ovine brucellosis with culling.
Nannyonga, B; Mwanga, G G; Luboobi, L S
2015-01-01
A mathematical model is used to study the dynamics of ovine brucellosis when transmitted directly from infected individual, through contact with a contaminated environment or vertically through mother to child. The model developed by Aïnseba et al. [A model for ovine brucellosis incorporating direct and indirect transmission, J. Biol. Dyn. 4 (2010), pp. 2-11. Available at http://www.math.u-bordeaux1.fr/?pmagal100p/papers/BBM-JBD09.pdf. Accessed 3 July 2012] was modified to include culling and then used to determine important parameters in the spread of human brucellosis using sensitivity analysis. An optimal control analysis was performed on the model to determine the best way to control such as a disease in the population. Three time-dependent controls to prevent exposure, cull the infected and reduce environmental transmission were used to set up to minimize infection at a minimum cost. PMID:26105034
Finite element solution of optimal control problems with state-control inequality constraints
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.
1992-01-01
It is demonstrated that the weak Hamiltonian finite-element formulation is amenable to the solution of optimal control problems with inequality constraints which are functions of both state and control variables. Difficult problems can be treated on account of the ease with which algebraic equations can be generated before having to specify the problem. These equations yield very accurate solutions. Owing to the sparse structure of the resulting Jacobian, computer solutions can be obtained quickly when the sparsity is exploited.
A Transformation Approach to Optimal Control Problems with Bounded State Variables
NASA Technical Reports Server (NTRS)
Hanafy, Lawrence Hanafy
1971-01-01
A technique is described and utilized in the study of the solutions to various general problems in optimal control theory, which are converted in to Lagrange problems in the calculus of variations. This is accomplished by mapping certain properties in Euclidean space onto closed control and state regions. Nonlinear control problems with a unit m cube as control region and unit n cube as state region are considered.
Variational principles and optimal solutions of the inverse problems of creep bending of plates
NASA Astrophysics Data System (ADS)
Bormotin, K. S.; Oleinikov, A. I.
2012-09-01
It is shown that inverse problems of steady-state creep bending of plates in both the geometrically linear and nonlinear formulations can be represented in a variational formulation. Steady-state values of the obtained functionals corresponding to the solutions of the problems of inelastic deformation and elastic unloading are determined by applying a finite element procedure to the functionals. Optimal laws of creep deformation are formulated using the criterion of minimizing damage in the functionals of the inverse problems. The formulated problems are reduced to the problems solved by the finite element method using MSC.Marc software.
The Sizing and Optimization Language, (SOL): Computer language for design problems
NASA Technical Reports Server (NTRS)
Lucas, Stephen H.; Scotti, Stephen J.
1988-01-01
The Sizing and Optimization Language, (SOL), a new high level, special purpose computer language was developed to expedite application of numerical optimization to design problems and to make the process less error prone. SOL utilizes the ADS optimization software and provides a clear, concise syntax for describing an optimization problem, the OPTIMIZE description, which closely parallels the mathematical description of the problem. SOL offers language statements which can be used to model a design mathematically, with subroutines or code logic, and with existing FORTRAN routines. In addition, SOL provides error checking and clear output of the optimization results. Because of these language features, SOL is best suited to model and optimize a design concept when the model consits of mathematical expressions written in SOL. For such cases, SOL's unique syntax and error checking can be fully utilized. SOL is presently available for DEC VAX/VMS systems. A SOL package is available which includes the SOL compiler, runtime library routines, and a SOL reference manual.
NASA Technical Reports Server (NTRS)
Tapia, R. A.; Vanrooy, D. L.
1976-01-01
A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.
Optimization of location routing inventory problem with transshipment
NASA Astrophysics Data System (ADS)
Ghani, Nor Edayu Abd; Shariff, S. Sarifah Radiah; Zahari, Siti Meriam
2015-05-01
Location Routing Inventory Problem (LRIP) is a collaboration of the three components in the supply chain. It is confined by location-allocation, vehicle routing and inventory management. The aim of the study is to minimize the total system cost in the supply chain. Transshipment is introduced in order to allow the products to be shipped to a customer who experiences a shortage, either directly from the supplier or from another customer. In the study, LRIP is introduced with the transshipment (LRIPT) and customers act as the transshipment points. We select the transshipment point by using the p-center and we present the results in two divisions of cases. Based on the analysis, the results indicated that LRIPT performed well compared to LRIP.
Active Batch Selection via Convex Relaxations with Guaranteed Solution Bounds.
Chakraborty, Shayok; Balasubramanian, Vineeth; Sun, Qian; Panchanathan, Sethuraman; Ye, Jieping
2015-10-01
Active learning techniques have gained popularity to reduce human effort in labeling data instances for inducing a classifier. When faced with large amounts of unlabeled data, such algorithms automatically identify the exemplar instances for manual annotation. More recently, there have been attempts towards a batch mode form of active learning, where a batch of data points is simultaneously selected from an unlabeled set. In this paper, we propose two novel batch mode active learning (BMAL) algorithms: BatchRank and BatchRand. We first formulate the batch selection task as an NP-hard optimization problem; we then propose two convex relaxations, one based on linear programming and the other based on semi-definite programming to solve the batch selection problem. Finally, a deterministic bound is derived on the solution quality for the first relaxation and a probabilistic bound for the second. To the best of our knowledge, this is the first research effort to derive mathematical guarantees on the solution quality of the BMAL problem. Our extensive empirical studies on 15 binary, multi-class and multi-label challenging datasets corroborate that the proposed algorithms perform at par with the state-of-the-art techniques, deliver high quality solutions and are robust to real-world issues like label noise and class imbalance. PMID:26353181
NASA Astrophysics Data System (ADS)
Tang, Yuchao
2015-03-01
Computed tomography (CT) image reconstruction problems can be solved by finding the minimization of a suitable objective function. The first-order methods for image reconstruction in CT have been popularized in recent years. These methods are interesting because they need only the first derivative information of the objective function and can solve non-smooth regularization functions. In this paper, we consider a constrained optimization problem which often appeared in the CT image reconstruction problems. For the unconstrained case, it has been studied recently. We dedicate to propose an efficient algorithm to solve the constrained optimization problem. Numerical experiments to image reconstruction benchmark problem show that the proposed algorithms can produce better reconstructed images in signal-to-noise than the original algorithm and other state-of-the-art methods.
Cost-Optimal Operation of Energy Storage Units: Benefits of a Problem-Specific Approach
Siemer, Lars; Kleinhans, David
2015-01-01
The integration of large shares of electricity produced by non-dispatchable Renewable Energy Sources (RES) leads to an increasingly volatile energy generation side, with temporary local overproduction. The application of energy storage units has the potential to use this excess electricity from RES efficiently and to prevent curtailment. The objective of this work is to calculate cost-optimal charging strategies for energy storage units used as buffers. For this purpose, a new mathematical optimization method is presented that is applicable to general storage-related problems. Due to a tremendous gain in efficiency of this method compared with standard solvers and proven optimality, calculations of complex problems as well as a high-resolution sensitivity analysis of multiple system combinations are feasible within a very short time. As an example technology, Power-to-Heat converters used in combination with thermal storage units are investigated in detail and optimal system configurations, including storage ...
A novel geometric approach to binary classification based on scaled convex hulls.
Liu, Zhenbing; Liu, J G; Pan, Chao; Wang, Guoyou
2009-07-01
Geometric methods are very intuitive and provide a theoretical foundation to many optimization problems in the fields of pattern recognition and machine learning. In this brief, the notion of scaled convex hull (SCH) is defined and a set of theoretical results are exploited to support it. These results allow the existing nearest point algorithms to be directly applied to solve both the separable and nonseparable classification problems successfully and efficiently. Then, the popular S-K algorithm has been presented to solve the nonseparable problems in the context of the SCH framework. The theoretical analysis and some experiments show that the proposed method may achieve better performance than the state-of-the-art methods in terms of the number of kernel evaluations and the execution time. PMID:19482572
Convex Programming Tools for Disjunctive Programs
Soares, JoÃ£o LuÃs Cardoso
region is the con- vex hull of the union of convex sets. The objective function is also convex conceptualizing a Branch-and-cut algorithm for mixed-integer convex programming. 1 Introduction The processConvex Programming Tools for Disjunctive Programs Jo~ao Soares, Departamento de Matem
Probabilistic Convex Hull Queries over Uncertain Data
Ng, Wilfred Siu Hung
to verify the efficiency of our algorithms for answering PCH queries. Index Terms--Convex hull, uncertain, it is not a point on the convex hull as it does not decide the polygon shape. A lot of algorithms have been proposed for convex hull computation, such as Andrew's Monotone Chain algorithm [6], which finds the convex hull
Vortex generator design for aircraft inlet distortion as a numerical optimization problem
NASA Technical Reports Server (NTRS)
Anderson, Bernhard H.; Levy, Ralph
1991-01-01
Aerodynamic compatibility of aircraft/inlet/engine systems is a difficult design problem for aircraft that must operate in many different flight regimes. Takeoff, subsonic cruise, supersonic cruise, transonic maneuvering, and high altitude loiter each place different constraints on inlet design. Vortex generators, small wing like sections mounted on the inside surfaces of the inlet duct, are used to control flow separation and engine face distortion. The design of vortex generator installations in an inlet is defined as a problem addressable by numerical optimization techniques. A performance parameter is suggested to account for both inlet distortion and total pressure loss at a series of design flight conditions. The resulting optimization problem is difficult since some of the design parameters take on integer values. If numerical procedures could be used to reduce multimillion dollar development test programs to a small set of verification tests, numerical optimization could have a significant impact on both cost and elapsed time to design new aircraft.
Using the PORS Problems to Examine Evolutionary Optimization of Multiscale Systems
Reinhart, Zachary; Molian, Vaelan; Bryden, Kenneth
2013-01-01
Nearly all systems of practical interest are composed of parts assembled across multiple scales. For example, an agrodynamic system is composed of flora and fauna on one scale; soil types, slope, and water runoff on another scale; and management practice and yield on another scale. Or consider an advanced coal-fired power plant: combustion and pollutant formation occurs on one scale, the plant components on another scale, and the overall performance of the power system is measured on another. In spite of this, there are few practical tools for the optimization of multiscale systems. This paper examines multiscale optimization of systems composed of discrete elements using the plus-one-recall-store (PORS) problem as a test case or study problem for multiscale systems. From this study, it is found that by recognizing the constraints and patterns present in discrete multiscale systems, the solution time can be significantly reduced and much more complex problems can be optimized.
Relationship Between MP and DPP for the Stochastic Optimal Control Problem of Jump Diffusions
Shi Jingtao Wu, Zhen
2011-04-15
This paper is concerned with the stochastic optimal control problem of jump diffusions. The relationship between stochastic maximum principle and dynamic programming principle is discussed. Without involving any derivatives of the value function, relations among the adjoint processes, the generalized Hamiltonian and the value function are investigated by employing the notions of semijets evoked in defining the viscosity solutions. Stochastic verification theorem is also given to verify whether a given admissible control is optimal.
Stochastic learning via optimizing the variational inequalities.
Tao, Qing; Gao, Qian-Kun; Chu, De-Jun; Wu, Gao-Wei
2014-10-01
A wide variety of learning problems can be posed in the framework of convex optimization. Many efficient algorithms have been developed based on solving the induced optimization problems. However, there exists a gap between the theoretically unbeatable convergence rate and the practically efficient learning speed. In this paper, we use the variational inequality (VI) convergence to describe the learning speed. To this end, we avoid the hard concept of regret in online learning and directly discuss the stochastic learning algorithms. We first cast the regularized learning problem as a VI. Then, we present a stochastic version of alternating direction method of multipliers (ADMMs) to solve the induced VI. We define a new VI-criterion to measure the convergence of stochastic algorithms. While the rate of convergence for any iterative algorithms to solve nonsmooth convex optimization problems cannot be better than O(1/?t), the proposed stochastic ADMM (SADMM) is proved to have an O(1/t) VI-convergence rate for the l1-regularized hinge loss problems without strong convexity and smoothness. The derived VI-convergence results also support the viewpoint that the standard online analysis is too loose to analyze the stochastic setting properly. The experiments demonstrate that SADMM has almost the same performance as the state-of-the-art stochastic learning algorithms but its O(1/t) VI-convergence rate is capable of tightly characterizing the real learning speed. PMID:25291732
Hoelder Continuity of Adjoint States and Optimal Controls for State Constrained Problems
Bettiol, Piernicola Frankowska, Helene
2008-02-15
We investigate Hoelder regularity of adjoint states and optimal controls for a Bolza problem under state constraints. We start by considering any optimal solution satisfying the constrained maximum principle in its normal form and we show that whenever the associated Hamiltonian function is smooth enough and has some monotonicity properties in the directions normal to the constraints, then both the adjoint state and optimal trajectory enjoy Hoelder type regularity. More precisely, we prove that if the state constraints are smooth, then the adjoint state and the derivative of the optimal trajectory are Hoelder continuous, while they have the two sided lower Hoelder continuity property for less regular constraints. Finally, we provide sufficient conditions for Hoelder type regularity of optimal controls.
Tahvili, Sahar; Österberg, Jonas; Silvestrov, Sergei; Biteus, Jonas
2014-12-10
One of the most important factors in the operations of many cooperations today is to maximize profit and one important tool to that effect is the optimization of maintenance activities. Maintenance activities is at the largest level divided into two major areas, corrective maintenance (CM) and preventive maintenance (PM). When optimizing maintenance activities, by a maintenance plan or policy, we seek to find the best activities to perform at each point in time, be it PM or CM. We explore the use of stochastic simulation, genetic algorithms and other tools for solving complex maintenance planning optimization problems in terms of a suggested framework model based on discrete event simulation.
A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem
NASA Technical Reports Server (NTRS)
Hughes, Steven P.; Mailhe, Laurie M.; Guzman, Jose J.
2002-01-01
In this paper we present a comparison of optimization approaches to the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP), Quasi-Newton, Simplex, Genetic Algorithms, and Simulated Annealing. Each method is applied to a variety of test cases including, circular to circular coplanar orbits, LEO to GEO, and orbit phasing in highly elliptic orbits. We also compare different constrained optimization routines on complex orbit rendezvous problems with complicated, highly nonlinear constraints.
Solution to Electric Power Dispatch Problem Using Fuzzy Particle Swarm Optimization Algorithm
NASA Astrophysics Data System (ADS)
Chaturvedi, D. K.; Kumar, S.
2015-03-01
This paper presents the application of fuzzy particle swarm optimization to constrained economic load dispatch (ELD) problem of thermal units. Several factors such as quadratic cost functions with valve point loading, ramp rate limits and prohibited operating zone are considered in the computation models. The Fuzzy particle swarm optimization (FPSO) provides a new mechanism to avoid premature convergence problem. The performance of proposed algorithm is evaluated on four test systems. Results obtained by proposed method have been compared with those obtained by PSO method and literature results. The experimental results show that proposed FPSO method is capable of obtaining minimum fuel costs in fewer numbers of iterations.
VeriQuickhull: fast sequential and parallel algorithms for computing the planar convex hull
Sambasivam, Mashilamani
1999-01-01
Computing the convex hull of a set of points in the plane is one of the most studied problems in computational geometry. The Quickhull algorithm is a popular convex hull algorithm. While the main structure of Quickhull is axed, many different...
Lipschitzian Regularity of Minimizers for Optimal Control Problems with Control-Affine Dynamics
Sarychev, A. V.; Torres, D. F. M. delfim@mat.ua.pt
2000-03-15
We study the Lagrange Problem of Optimal Control with a functional {integral}{sub a}{sup b}L(t,x(t),u(t)) dt and control-affine dynamics x-dot= f(t,x) + g(t,x)u and (a priori) unconstrained control u element of bf R{sup m}. We obtain conditions under which the minimizing controls of the problem are bounded-a fact which is crucial for the applicability of many necessary optimality conditions, like, for example, the Pontryagin Maximum Principle. As a corollary we obtain conditions for the Lipschitzian regularity of minimizers of the Basic Problem of the Calculus of Variations and of the Problem of the Calculus of Variations with higher-order derivatives.
Men, H. Nguyen, N.C. Freund, R.M. Parrilo, P.A. Peraire, J.
2010-05-20
In this paper, we consider the optimal design of photonic crystal structures for two-dimensional square lattices. The mathematical formulation of the bandgap optimization problem leads to an infinite-dimensional Hermitian eigenvalue optimization problem parametrized by the dielectric material and the wave vector. To make the problem tractable, the original eigenvalue problem is discretized using the finite element method into a series of finite-dimensional eigenvalue problems for multiple values of the wave vector parameter. The resulting optimization problem is large-scale and non-convex, with low regularity and non-differentiable objective. By restricting to appropriate eigenspaces, we reduce the large-scale non-convex optimization problem via reparametrization to a sequence of small-scale convex semidefinite programs (SDPs) for which modern SDP solvers can be efficiently applied. Numerical results are presented for both transverse magnetic (TM) and transverse electric (TE) polarizations at several frequency bands. The optimized structures exhibit patterns which go far beyond typical physical intuition on periodic media design.
Convex polytopes and quantum separability
Holik, F.; Plastino, A.
2011-12-15
We advance a perspective of the entanglement issue that appeals to the Schlienz-Mahler measure [Phys. Rev. A 52, 4396 (1995)]. Related to it, we propose a criterium based on the consideration of convex subsets of quantum states. This criterium generalizes a property of product states to convex subsets (of the set of quantum states) that is able to uncover an interesting geometrical property of the separability property.
Application of an Optimized MacCormack-Type Scheme to Acoustic Scattering Problems
NASA Technical Reports Server (NTRS)
Hixon, Ray; Shih, S. H.; Mankbadi, Reda R.
1997-01-01
In this work, a new optimized MacCormack-type scheme, which is 4th order accurate in time and space, is applied to Problems 1 and 2 of Category 1. The performance of this new scheme is compared to that of the 2-4 MacCormack scheme, and results for Problems 1 and 2 of Category 1 are presented and compared to the exact solutions.
NASA Astrophysics Data System (ADS)
Berezkin, V. E.; Lotov, A. V.; Lotova, E. A.
2014-06-01
Methods for approximating the Edgeworth-Pareto hull (EPH) of the set of feasible criteria vectors in nonlinear multicriteria optimization problems are examined. The relative efficiency of two EPH approximation methods based on classical methods of searching for local extrema of convolutions of criteria is experimentally studied for a large-scale applied problem (with several hundred variables). A hybrid EPH approximation method combining classical and genetic approximation methods is considered.
Nash, Stephen G.
2013-11-11
The research focuses on the modeling and optimization of nanoporous materials. In systems with hierarchical structure that we consider, the physics changes as the scale of the problem is reduced and it can be important to account for physics at the fine level to obtain accurate approximations at coarser levels. For example, nanoporous materials hold promise for energy production and storage. A significant issue is the fabrication of channels within these materials to allow rapid diffusion through the material. One goal of our research is to apply optimization methods to the design of nanoporous materials. Such problems are large and challenging, with hierarchical structure that we believe can be exploited, and with a large range of important scales, down to atomistic. This requires research on large-scale optimization for systems that exhibit different physics at different scales, and the development of algorithms applicable to designing nanoporous materials for many important applications in energy production, storage, distribution, and use. Our research has two major research thrusts. The first is hierarchical modeling. We plan to develop and study hierarchical optimization models for nanoporous materials. The models have hierarchical structure, and attempt to balance the conflicting aims of model fidelity and computational tractability. In addition, we analyze the general hierarchical model, as well as the specific application models, to determine their properties, particularly those properties that are relevant to the hierarchical optimization algorithms. The second thrust was to develop, analyze, and implement a class of hierarchical optimization algorithms, and apply them to the hierarchical models we have developed. We adapted and extended the optimization-based multigrid algorithms of Lewis and Nash to the optimization models exemplified by the hierarchical optimization model. This class of multigrid algorithms has been shown to be a powerful tool for solving discretized optimization models. Our optimization models are multi-level models, however. They are more general, involving different governing equations at each level. A major aspect of this project was the development of flexible software that can be used to solve a variety of hierarchical optimization problems.
An investigation of exploitation versus exploration in GBEA optimization of PORS 15 and 16 Problems
Koch, Kaelynn
2012-05-08
It was hypothesized that the variations in time to solution are driven by the competing mechanisms of exploration and exploitation.This thesis explores this hypothesis by examining two contrasting problems that embody the hypothesized tradeoff between exploration and exploitation. Plus one recall store (PORS) is an optimization problem based on the idea of a simple calculator with four buttons: plus, one, store, and recall. Integer addition and store are classified as operations, and one and memory recall are classified as terminals. The goal is to arrange a fixed number of keystrokes in a way that maximizes the numerical result. PORS 15 (15 keystrokes) represents the subset of difficult PORS problems and PORS 16 (16 keystrokes) represents the subset of PORS problems that are easiest to optimize. The goal of this work is to examine the tradeoff between exploitation and exploration in graph based evolutionary algorithm (GBEA) optimization. To do this, computational experiments are used to examine how solutions evolve in PORS 15 and 16 problems when solved using GBEAs. The experiment is comprised of three components; the graphs and the population, the evolutionary algorithm rule set, and the example problems. The complete, hypercube, and cycle graphs were used for this experiment. A fixed population size was used.
Bacanin, Nebojsa; Tuba, Milan
2014-01-01
Portfolio optimization (selection) problem is an important and hard optimization problem that, with the addition of necessary realistic constraints, becomes computationally intractable. Nature-inspired metaheuristics are appropriate for solving such problems; however, literature review shows that there are very few applications of nature-inspired metaheuristics to portfolio optimization problem. This is especially true for swarm intelligence algorithms which represent the newer branch of nature-inspired algorithms. No application of any swarm intelligence metaheuristics to cardinality constrained mean-variance (CCMV) portfolio problem with entropy constraint was found in the literature. This paper introduces modified firefly algorithm (FA) for the CCMV portfolio model with entropy constraint. Firefly algorithm is one of the latest, very successful swarm intelligence algorithm; however, it exhibits some deficiencies when applied to constrained problems. To overcome lack of exploration power during early iterations, we modified the algorithm and tested it on standard portfolio benchmark data sets used in the literature. Our proposed modified firefly algorithm proved to be better than other state-of-the-art algorithms, while introduction of entropy diversity constraint further improved results. PMID:24991645
2014-01-01
Portfolio optimization (selection) problem is an important and hard optimization problem that, with the addition of necessary realistic constraints, becomes computationally intractable. Nature-inspired metaheuristics are appropriate for solving such problems; however, literature review shows that there are very few applications of nature-inspired metaheuristics to portfolio optimization problem. This is especially true for swarm intelligence algorithms which represent the newer branch of nature-inspired algorithms. No application of any swarm intelligence metaheuristics to cardinality constrained mean-variance (CCMV) portfolio problem with entropy constraint was found in the literature. This paper introduces modified firefly algorithm (FA) for the CCMV portfolio model with entropy constraint. Firefly algorithm is one of the latest, very successful swarm intelligence algorithm; however, it exhibits some deficiencies when applied to constrained problems. To overcome lack of exploration power during early iterations, we modified the algorithm and tested it on standard portfolio benchmark data sets used in the literature. Our proposed modified firefly algorithm proved to be better than other state-of-the-art algorithms, while introduction of entropy diversity constraint further improved results. PMID:24991645
Masiero, Federica
2007-05-15
Semilinear elliptic partial differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. These results are applied to a stochastic optimal control problem with infinite horizon. Applications to controlled stochastic heat and wave equations are given.
Optimal constant in an L 2 extension problem and a proof of a conjecture of Ohsawa
NASA Astrophysics Data System (ADS)
Guan, Qi'An; Zhou, XiangYu
2015-01-01
In this paper, we solve the optimal constant problem in the setting of Ohsawa's generalized $L^{2}$ extension theorem. As applications, we prove a conjecture of Ohsawa and the extended Suita conjecture, we also establish some relations between Bergman kernel and logarithmic capacity on compact and open Riemann surfaces.
Statics and asymptotics of a price control limit: an optimal timing inventory problem
Haase, Markus
Statics and asymptotics of a price control limit: an optimal timing inventory problem R.O. Davies statics of the censor and show that W = W( , ) is increasing with variance and decreasing with drift; we an embedded commitment to receive a ...xed amount u of inventory (inputs for a production process
Ledzewicz, Urszula
Bifurcation of Singular Arcs in an Optimal Control Problem for Cancer Immune System Interactions equilibrium is discussed. I. INTRODUCTION We consider a mathematical model for cancer-immune system the interactions between cancer cell growth and the activity of the immune system during the development of cancer
Constrained Optimization Problems in Cost and Managerial Accounting--Spreadsheet Tools
ERIC Educational Resources Information Center
Amlie, Thomas T.
2009-01-01
A common problem addressed in Managerial and Cost Accounting classes is that of selecting an optimal production mix given scarce resources. That is, if a firm produces a number of different products, and is faced with scarce resources (e.g., limitations on labor, materials, or machine time), what combination of products yields the greatest profit…
Biogeography-Based Optimization and the Solution of the Power Flow Problem
Simon, Dan
absorbed by the loads plus the power losses that occur in the transmission system. Second, both the activeBiogeography-Based Optimization and the Solution of the Power Flow Problem Rick Rarick, Dan Simon and emigration between the islands. This paper presents an application of the BBO algorithm to the power flow
ORIGINAL ARTICLE Data driven surrogate-based optimization in the problem solving
Ramakrishnan, Naren
ORIGINAL ARTICLE Data driven surrogate-based optimization in the problem solving environment WBCSim model as closely as possible. This paper presents a data driven, surrogate-based opti- mization algorithms to build the surrogates and three different DOE techniques-- full factorial (FF), Latin hypercube
Optimization of Power in the Problems of Active Control of Sound
Optimization of Power in the Problems of Active Control of Sound J. Loncari´c 1 Los Alamos National, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous
Optimization of Power in the Problems of Active Control of Sound ?
Optimization of Power in the Problems of Active Control of Sound ? J. Lon#20;cari#19;c 1 Los Alamos that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls the overall absolute acoustic source strength. In the current paper, we minimize the power required
Genetic Algorithms with Elitism-Based Immigrants for Changing Optimization Problems
Yang, Shengxiang
Genetic Algorithms with Elitism-Based Immigrants for Changing Optimization Problems Shengxiang Yang.g., via random immigrants. This paper proposes an elitism-based immigrants scheme for genetic al- gorithms immigrants via mutation to replace the worst individuals in the current population. This way, the introduced
A multilevel, level-set method for optimizing eigenvalues in shape design problems
Ferguson, Thomas S.
A multilevel, level-set method for optimizing eigenvalues in shape design problems E. Haber July 22 process and replace the eigenvalue equation with the inverse iteration. We then compute the gradients of obtaining the eigenvalue is divorced from the process of calculating its derivative. The advantages of our
Adaptive finite element methods for PDE-constrained optimal control problems
Adaptive finite element methods for PDE-constrained optimal control problems R. Becker1 , M. Braack¨at Heidelberg 3 Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences is discretized by a finite element Galerkin method. The accuracy of the discretization is controlled by residual
NASA Astrophysics Data System (ADS)
Ivashkin, V. V.; Krylov, I. V.
2015-09-01
A method to optimize the flight trajectories to the asteroid Apophis that allows reliably to form a set of Pontryagin extremals for various boundary conditions of the flight, as well as effectively to search for a global problem optimum amongst its elements, is developed.
IMPROVING THE PERFORMANCE OF THE HOPFIELD NETWORK FOR SOLVING OPTIMIZATION PROBLEMS
Martinez, Tony R.
optimization problems have been developed and evaluated in this work. The first approach uses a new activation the relaxation process so that the network can be relaxed at a proper rate. The third approach applies a new the performance of the network. Among them, the new relaxation procedure achieved the highest improvement
NASA Astrophysics Data System (ADS)
Evtushenko, Yu. G.; Posypkin, M. A.
2013-02-01
The nonuniform covering method is applied to multicriteria optimization problems. The ?-Pareto set is defined, and its properties are examined. An algorithm for constructing an ?-Pareto set with guaranteed accuracy ? is described. The efficiency of implementing this approach is discussed, and numerical results are presented.
An optimal control problem arising from a dengue disease transmission model.
Aldila, Dipo; Götz, Thomas; Soewono, Edy
2013-03-01
An optimal control problem for a host-vector Dengue transmission model is discussed here. In the model, treatments with mosquito repellent are given to adults and children and those who undergo treatment are classified in treated compartments. With this classification, the model consists of 11 dynamic equations. The basic reproductive ratio that represents the epidemic indicator is obtained from the largest eigenvalue of the next generation matrix. The optimal control problem is designed with four control parameters, namely the treatment rates for children and adult compartments, and the drop-out rates from both compartments. The cost functional accounts for the total number of the infected persons, the cost of the treatment, and the cost related to reducing the drop-out rates. Numerical results for the optimal controls and the related dynamics are shown for the case of epidemic prevention and outbreak reduction strategies. PMID:23274179
Evaluation of large-scale optimization problems on vector and parallel architectures
Averick, B.M.; More, J.J.
1994-11-01
The authors examine the importance of problem formulation for the solution of large-scale optimization problems on high-performance architectures. Limited memory variable metric methods are used to illustrate performance issues. It is shown that the performance of these algorithms is drastically affected by application implementation. Model applications are drawn from the MINPACK-2 test problem collection, with numerical results from a super-scalar architecture (IBM RS6000/370), a vector architecture (CRAY-2), and a massively parallel architecture (Intel DELTA).
Inverse problems and optimal experiment design in unsteady heat transfer processes identification
NASA Technical Reports Server (NTRS)
Artyukhin, Eugene A.
1991-01-01
Experimental-computational methods for estimating characteristics of unsteady heat transfer processes are analyzed. The methods are based on the principles of distributed parameter system identification. The theoretical basis of such methods is the numerical solution of nonlinear ill-posed inverse heat transfer problems and optimal experiment design problems. Numerical techniques for solving problems are briefly reviewed. The results of the practical application of identification methods are demonstrated when estimating effective thermophysical characteristics of composite materials and thermal contact resistance in two-layer systems.
Digital program for solving the linear stochastic optimal control and estimation problem
NASA Technical Reports Server (NTRS)
Geyser, L. C.; Lehtinen, B.
1975-01-01
A computer program is described which solves the linear stochastic optimal control and estimation (LSOCE) problem by using a time-domain formulation. The LSOCE problem is defined as that of designing controls for a linear time-invariant system which is disturbed by white noise in such a way as to minimize a performance index which is quadratic in state and control variables. The LSOCE problem and solution are outlined; brief descriptions are given of the solution algorithms, and complete descriptions of each subroutine, including usage information and digital listings, are provided. A test case is included, as well as information on the IBM 7090-7094 DCS time and storage requirements.
Haber, Eldad
2014-03-17
The focus of research was: Developing adaptive mesh for the solution of Maxwell's equations; Developing a parallel framework for time dependent inverse Maxwell's equations; Developing multilevel methods for optimization problems with inequal- ity constraints; A new inversion code for inverse Maxwell's equations in the 0th frequency (DC resistivity); A new inversion code for inverse Maxwell's equations in low frequency regime. Although the research concentrated on electromagnetic forward and in- verse problems the results of the research was applied to the problem of image registration.
Electronic neural network for solving traveling salesman and similar global optimization problems
NASA Technical Reports Server (NTRS)
Thakoor, Anilkumar P. (inventor); Moopenn, Alexander W. (inventor); Duong, Tuan A. (inventor); Eberhardt, Silvio P. (inventor)
1993-01-01
This invention is a novel high-speed neural network based processor for solving the 'traveling salesman' and other global optimization problems. It comprises a novel hybrid architecture employing a binary synaptic array whose embodiment incorporates the fixed rules of the problem, such as the number of cities to be visited. The array is prompted by analog voltages representing variables such as distances. The processor incorporates two interconnected feedback networks, each of which solves part of the problem independently and simultaneously, yet which exchange information dynamically.
Mittal, Shashi
In this paper, we present a general framework for designing approximation schemes for combinatorial optimization problems in which the objective function is a combination of more than one function. Examples of such problems ...
Energy optimization in mobile sensor networks
NASA Astrophysics Data System (ADS)
Yu, Shengwei
Mobile sensor networks are considered to consist of a network of mobile robots, each of which has computation, communication and sensing capabilities. Energy efficiency is a critical issue in mobile sensor networks, especially when mobility (i.e., locomotion control), routing (i.e., communications) and sensing are unique characteristics of mobile robots for energy optimization. This thesis focuses on the problem of energy optimization of mobile robotic sensor networks, and the research results can be extended to energy optimization of a network of mobile robots that monitors the environment, or a team of mobile robots that transports materials from stations to stations in a manufacturing environment. On the energy optimization of mobile robotic sensor networks, our research focuses on the investigation and development of distributed optimization algorithms to exploit the mobility of robotic sensor nodes for network lifetime maximization. In particular, the thesis studies these five problems: 1. Network-lifetime maximization by controlling positions of networked mobile sensor robots based on local information with distributed optimization algorithms; 2. Lifetime maximization of mobile sensor networks with energy harvesting modules; 3. Lifetime maximization using joint design of mobility and routing; 4. Optimal control for network energy minimization; 5. Network lifetime maximization in mobile visual sensor networks. In addressing the first problem, we consider only the mobility strategies of the robotic relay nodes in a mobile sensor network in order to maximize its network lifetime. By using variable substitutions, the original problem is converted into a convex problem, and a variant of the sub-gradient method for saddle-point computation is developed for solving this problem. An optimal solution is obtained by the method. Computer simulations show that mobility of robotic sensors can significantly prolong the lifetime of the whole robotic sensor network while consuming negligible amount of energy for mobility cost. For the second problem, the problem is extended to accommodate mobile robotic nodes with energy harvesting capability, which makes it a non-convex optimization problem. The non-convexity issue is tackled by using the existing sequential convex approximation method, based on which we propose a novel procedure of modified sequential convex approximation that has fast convergence speed. For the third problem, the proposed procedure is used to solve another challenging non-convex problem, which results in utilizing mobility and routing simultaneously in mobile robotic sensor networks to prolong the network lifetime. The results indicate that joint design of mobility and routing has an edge over other methods in prolonging network lifetime, which is also the justification for the use of mobility in mobile sensor networks for energy efficiency purpose. For the fourth problem, we include the dynamics of the robotic nodes in the problem by modeling the networked robotic system using hybrid systems theory. A novel distributed method for the networked hybrid system is used to solve the optimal moving trajectories for robotic nodes and optimal network links, which are not answered by previous approaches. Finally, the fact that mobility is more effective in prolonging network lifetime for a data-intensive network leads us to apply our methods to study mobile visual sensor networks, which are useful in many applications. We investigate the joint design of mobility, data routing, and encoding power to help improving the video quality while maximizing the network lifetime. This study leads to a better understanding of the role mobility can play in data-intensive surveillance sensor networks.
A new convexity measure for polygons.
Zunic, Jovisa; Rosin, Paul L
2004-07-01
Abstract-Convexity estimators are commonly used in the analysis of shape. In this paper, we define and evaluate a new convexity measure for planar regions bounded by polygons. The new convexity measure can be understood as a "boundary-based" measure and in accordance with this it is more sensitive to measured boundary defects than the so called "area-based" convexity measures. When compared with the convexity measure defined as the ratio between the Euclidean perimeter of the convex hull of the measured shape and the Euclidean perimeter of the measured shape then the new convexity measure also shows some advantages-particularly for shapes with holes. The new convexity measure has the following desirable properties: 1) the estimated convexity is always a number from (0, 1], 2) the estimated convexity is 1 if and only if the measured shape is convex, 3) there are shapes whose estimated convexity is arbitrarily close to 0, 4) the new convexity measure is invariant under similarity transformations, and 5) there is a simple and fast procedure for computing the new convexity measure. PMID:18579950
Limitations of Parallel Global Optimization for Large-Scale Human Movement Problems
Koh, Byung-Il; Reinbolt, Jeffrey A.; George, Alan D.; Haftka, Raphael T.; Fregly, Benjamin J.
2009-01-01
Global optimization algorithms (e.g., simulated annealing, genetic, and particle swarm) have been gaining popularity in biomechanics research, in part due to advances in parallel computing. To date, such algorithms have only been applied to small- or medium-scale optimization problems (< 100 design variables). This study evaluates the applicability of a parallel particle swarm global optimization algorithm to large-scale human movement problems. The evaluation was performed using two large-scale (660 design variables) optimization problems that utilized a dynamic, 27 degree-of-freedom, full-body gait model to predict new gait motions from a nominal gait motion. Both cost functions minimized a quantity that reduced the knee adduction torque. The first one minimized foot path errors corresponding to an increased toe out angle of 15 deg, while the second one minimized the knee adduction torque directly without changing the foot path. Constraints on allowable changes in trunk orientation, joint angles, joint torques, centers of pressure, and ground reactions were handled using a penalty method. For both problems, a single run with a gradient-based nonlinear least squares algorithm found a significantly better solution than did 10 runs with the global particle swarm algorithm. Due to the penalty terms, the physically-realistic gradient-based solutions were located within a narrow “channel” in design space that was difficult to enter without gradient information. Researchers should exercise caution when extrapolating the performance of parallel global optimizers to human movement problems with hundreds of design variables, especially when penalty terms are included in the cost function. PMID:19036629
Convex Configurations In Free Boundary Problems
2002-10-30
I thank all my teachers and especially my diploma advisor Norair Arakelian for teaching me ..... One of the steps in the proof of (8 ) is the following fact. .... Khim., 12 (1938), 100–105 (in Russian; English translation in “Collected Works of Ya.
A non-convex gradient fidelity-based variational model for image contrast enhancement
NASA Astrophysics Data System (ADS)
Liu, Qiegen; Liu, Jianbo; Xiong, Biao; Liang, Dong
2014-12-01
We propose a novel image contrast enhancement method via non-convex gradient fidelity-based (NGF) variational model which consists of the data fidelity term and the NGF regularization. The NGF prior assumes that the gradient of the desired image is close to the multiplication of the gradient of the original image by a scale factor, which is adaptively proportional to the difference of their gradients. The presented variational model can be viewed as a data-driven alpha-rooting method in the gradient domain. An augmented Lagrangian method is proposed to address this optimization issue by first transforming the unconstrained problem to an equivalent constrained problem and then applying an alternating direction method to iteratively solve the subproblems. Experimental results on a number of images consistently demonstrate that the proposed algorithm can efficiently obtain visual pleasure results and achieve favorable performance than the current state-of-the-art methods.
A capacity scaling algorithm for convex cost submodular flows
Iwata, Satoru
1996-12-31
This paper presents a scaling scheme for submodular functions. A small but strictly submodular function is added before scaling so that the resulting functions should be submodular. This scaling scheme leads to a weakly polynomial algorithm to solve minimum cost integral submodular flow problems with separable convex cost functions, provided that an oracle for exchange capacities are available.
Gyroscopic Forces and Collision Avoidance with Convex Obstacles
Marsden, Jerrold
Gyroscopic Forces and Collision Avoidance with Convex Obstacles Dong Eui Chang1 and Jerrold E, CA 91125; marsden@cds.caltech.edu Summary. This paper introduces gyroscopic forces as an tool- ular gyroscopic control forces--in the problem of collision and obstacle avoid- ance. We are also
A Hybrid Optimization Method for Solving Bayesian Inverse Problems under Uncertainty
Zhang, Kai; Wang, Zengfei; Zhang, Liming; Yao, Jun; Yan, Xia
2015-01-01
In this paper, we investigate the application of a new method, the Finite Difference and Stochastic Gradient (Hybrid method), for history matching in reservoir models. History matching is one of the processes of solving an inverse problem by calibrating reservoir models to dynamic behaviour of the reservoir in which an objective function is formulated based on a Bayesian approach for optimization. The goal of history matching is to identify the minimum value of an objective function that expresses the misfit between the predicted and measured data of a reservoir. To address the optimization problem, we present a novel application using a combination of the stochastic gradient and finite difference methods for solving inverse problems. The optimization is constrained by a linear equation that contains the reservoir parameters. We reformulate the reservoir model’s parameters and dynamic data by operating the objective function, the approximate gradient of which can guarantee convergence. At each iteration step, we obtain the relatively ‘important’ elements of the gradient, which are subsequently substituted by the values from the Finite Difference method through comparing the magnitude of the components of the stochastic gradient, which forms a new gradient, and we subsequently iterate with the new gradient. Through the application of the Hybrid method, we efficiently and accurately optimize the objective function. We present a number numerical simulations in this paper that show that the method is accurate and computationally efficient. PMID:26252392
The genealogy of convex solids
Domokos, Gabor; Szabó, Timea
2012-01-01
The shape of homogeneous, smooth convex bodies as described by the Euclidean distance from the center of gravity represents a rather restricted class M_C of Morse-Smale functions on S^2. Here we show that even M_C exhibits the complexity known for general Morse-Smale functions on S^2 by exhausting all combinatorial possibilities: every 2-colored quadrangulation of the sphere is isomorphic to a suitably represented Morse-Smale complex associated with a function in M_C (and vice versa). We prove our claim by an inductive algorithm, starting from the path graph P_2 and generating convex bodies corresponding to quadrangulations with increasing number of vertices by performing each combinatorially possible vertex splitting by a convexity- preserving local manipulation of the surface. Since convex bodies carrying Morse-Smale complexes isomorphic to P_2 exist, this algorithm not only proves our claim but also defines a hierarchical order among convex solids and general- izes the known classification scheme in [35], ...
Finding Convex Hulls Using Quickhull on the GPU
Tzeng, Stanley
2012-01-01
We present a convex hull algorithm that is accelerated on commodity graphics hardware. We analyze and identify the hurdles of writing a recursive divide and conquer algorithm on the GPU and divise a framework for representing this class of problems. Our framework transforms the recursive splitting step into a permutation step that is well-suited for graphics hardware. Our convex hull algorithm of choice is Quickhull. Our parallel Quickhull implementation (for both 2D and 3D cases) achieves an order of magnitude speedup over standard computational geometry libraries.
Maurer, Helmut
Sensitivity Analysis of Optimal Control Problems with BangÂBang Controls Jang-Ho Robert Kim, Helmut control can be locally embedded into a parametric family of optimal bangÂbang controls where the switching Sensitivity analysis for parametric optimal control prob- lems has been studied extensively in the case
Legendre spectral-collocation method for solving some types of fractional optimal control problems.
Sweilam, Nasser H; Al-Ajami, Tamer M
2015-05-01
In this paper, the Legendre spectral-collocation method was applied to obtain approximate solutions for some types of fractional optimal control problems (FOCPs). The fractional derivative was described in the Caputo sense. Two different approaches were presented, in the first approach, necessary optimality conditions in terms of the associated Hamiltonian were approximated. In the second approach, the state equation was discretized first using the trapezoidal rule for the numerical integration followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Illustrative examples were included to demonstrate the validity and applicability of the proposed techniques. PMID:26257937
NASA Technical Reports Server (NTRS)
Markopoulos, N.; Calise, A. J.
1993-01-01
The class of all piecewise time-continuous controllers tracking a given hypersurface in the state space of a dynamical system can be split by the present transformation technique into two disjoint classes; while the first of these contains all controllers which track the hypersurface in finite time, the second contains all controllers that track the hypersurface asymptotically. On this basis, a reformulation is presented for optimal control problems involving state-variable inequality constraints. If the state constraint is regarded as 'soft', there may exist controllers which are asymptotic, two-sided, and able to yield the optimal value of the performance index.
Improved Fractal Space Filling Curves Hybrid Optimization Algorithm for Vehicle Routing Problem
Yue, Yi-xiang; Zhang, Tong; Yue, Qun-xing
2015-01-01
Vehicle Routing Problem (VRP) is one of the key issues in optimization of modern logistics system. In this paper, a modified VRP model with hard time window is established and a Hybrid Optimization Algorithm (HOA) based on Fractal Space Filling Curves (SFC) method and Genetic Algorithm (GA) is introduced. By incorporating the proposed algorithm, SFC method can find an initial and feasible solution very fast; GA is used to improve the initial solution. Thereafter, experimental software was developed and a large number of experimental computations from Solomon's benchmark have been studied. The experimental results demonstrate the feasibility and effectiveness of the HOA. PMID:26167171
On large-scale nonlinear programming techniques for solving optimal control problems
Faco, J.L.D.
1994-12-31
The formulation of decision problems by Optimal Control Theory allows the consideration of their dynamic structure and parameters estimation. This paper deals with techniques for choosing directions in the iterative solution of discrete-time optimal control problems. A unified formulation incorporates nonlinear performance criteria and dynamic equations, time delays, bounded state and control variables, free planning horizon and variable initial state vector. In general they are characterized by a large number of variables, mostly when arising from discretization of continuous-time optimal control or calculus of variations problems. In a GRG context the staircase structure of the jacobian matrix of the dynamic equations is exploited in the choice of basic and super basic variables and when changes of basis occur along the process. The search directions of the bound constrained nonlinear programming problem in the reduced space of the super basic variables are computed by large-scale NLP techniques. A modified Polak-Ribiere conjugate gradient method and a limited storage quasi-Newton BFGS method are analyzed and modifications to deal with the bounds on the variables are suggested based on projected gradient devices with specific linesearches. Some practical models are presented for electric generation planning and fishery management, and the application of the code GRECO - Gradient REduit pour la Commande Optimale - is discussed.
A finite element based method for solution of optimal control problems
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.; Calise, Anthony J.
1989-01-01
A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.
[Type text] Convex Optimization + DEA Courses
Hall, Julian
To use the computing labs and (eduroam) wifi, you will be given a temporary University of Edinburgh service, EASE, https://www.ease.ed.ac.uk/register. Wifi: Wifi has been enabled on these natcor* accounts://vpnreg.ucs.ed.ac.uk/ease/selfreg.cgi. Note that this page is EASE protected so you cannot set a wifi password until you have first registered
Convex Hull of Arithmetic Automata
Leroux, Jérôme
2008-01-01
Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm computing the linear constraints defining these convex set is provided. Such an algorithm is useful for effectively extracting geometrical properties of the whole set of solutions of complex constraints symbolically represented by arithmetic automata.