Menu-Driven Solver Of Linear-Programming Problems
NASA Technical Reports Server (NTRS)
Viterna, L. A.; Ferencz, D.
1992-01-01
Program assists inexperienced user in formulating linear-programming problems. A Linear Program Solver (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).
Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution
Hamadameen, Abdulqader Othman; Zainuddin, Zaitul Marlizawati
2014-06-19
This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.
Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution
NASA Astrophysics Data System (ADS)
Hamadameen, Abdulqader Othman; Zainuddin, Zaitul Marlizawati
2014-06-01
This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α-. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen's method is employed to find a compromise solution, supported by illustrative numerical example.
NASA Astrophysics Data System (ADS)
Lachhwani, Kailash; Nehra, Suresh
2015-09-01
In this paper, we present modified fuzzy goal programming (FGP) approach and generalized MATLAB program for solving multi-level linear fractional programming problems (ML-LFPPs) based on with some major modifications in earlier FGP algorithms. In proposed modified FGP approach, solution preferences by the decision makers at each level are not considered and fuzzy goal for the decision vectors is defined using individual best solutions. The proposed modified algorithm as well as MATLAB program simplifies the earlier algorithm on ML-LFPP by eliminating solution preferences by the decision makers at each level, thereby avoiding difficulties associate with multi-level programming problems and decision deadlock situation. The proposed modified technique is simple, efficient and requires less computational efforts in comparison of earlier FGP techniques. Also, the proposed coding of generalized MATLAB program based on this modified approach for solving ML-LFPPs is the unique programming tool toward dealing with such complex mathematical problems with MATLAB. This software based program is useful and user can directly obtain compromise optimal solution of ML-LFPPs with it. The aim of this paper is to present modified FGP technique and generalized MATLAB program to obtain compromise optimal solution of ML-LFP problems in simple and efficient manner. A comparative analysis is also carried out with numerical example in order to show efficiency of proposed modified approach and to demonstrate functionality of MATLAB program.
Zhao, Yingfeng; Liu, Sanyang
2016-01-01
We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient. PMID:27547676
NASA Astrophysics Data System (ADS)
Vasant, P.; Ganesan, T.; Elamvazuthi, I.
2012-11-01
A fairly reasonable result was obtained for non-linear engineering problems using the optimization techniques such as neural network, genetic algorithms, and fuzzy logic independently in the past. Increasingly, hybrid techniques are being used to solve the non-linear problems to obtain better output. This paper discusses the use of neuro-genetic hybrid technique to optimize the geological structure mapping which is known as seismic survey. It involves the minimization of objective function subject to the requirement of geophysical and operational constraints. In this work, the optimization was initially performed using genetic programming, and followed by hybrid neuro-genetic programming approaches. Comparative studies and analysis were then carried out on the optimized results. The results indicate that the hybrid neuro-genetic hybrid technique produced better results compared to the stand-alone genetic programming method.
LP-DIT interchange tool for linear programming problems
Makowski, M.
1994-12-31
LP-DIT is a small library that provides an easy handling of LP problem data between a problem generator, solver and other modules (problem modification, generation of multi-criteria problem, report writers, etc). So far LP-DIT has been implemented with 4 LP (including one MIP) solvers and is being used as a module for model-based Decision Support System. LP-DIT will be released as a public domain soft-ware in the coming weeks.
An application of a linear programing technique to nonlinear minimax problems
NASA Technical Reports Server (NTRS)
Schiess, J. R.
1973-01-01
A differential correction technique for solving nonlinear minimax problems is presented. The basis of the technique is a linear programing algorithm which solves the linear minimax problem. By linearizing the original nonlinear equations about a nominal solution, both nonlinear approximation and estimation problems using the minimax norm may be solved iteratively. Some consideration is also given to improving convergence and to the treatment of problems with more than one measured quantity. A sample problem is treated with this technique and with the least-squares differential correction method to illustrate the properties of the minimax solution. The results indicate that for the sample approximation problem, the minimax technique provides better estimates than the least-squares method if a sufficient amount of data is used. For the sample estimation problem, the minimax estimates are better if the mathematical model is incomplete.
NASA Technical Reports Server (NTRS)
Tuey, R. C.
1972-01-01
Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.
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.
NASA Astrophysics Data System (ADS)
Takabe, Satoshi; Hukushima, Koji
2014-04-01
The typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover problem, which is a type of integer programming (IP) problem. To deal with LP and IP using statistical mechanics, a lattice-gas model on the Erdös-Rényi random graphs is analyzed by a replica method. It is found that the LP optimal solution is typically equal to that given by IP below the critical average degree c*=e in the thermodynamic limit. The critical threshold for LP = IP extends the previous result c = 1, and coincides with the replica symmetry-breaking threshold of the IP.
Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control
Gaitsgory, Vladimir; Rossomakhine, Sergey
2015-04-15
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.
A strictly improving linear programming alorithm based on a series of Phase 1 problems
Leichner, S.A.; Dantzig, G.B.; Davis, J.W.
1992-04-01
When used on degenerate problems, the simplex method often takes a number of degenerate steps at a particular vertex before moving to the next. In theory (although rarely in practice), the simplex method can actually cycle at such a degenerate point. Instead of trying to modify the simplex method to avoid degenerate steps, we have developed a new linear programming algorithm that is completely impervious to degeneracy. This new method solves the Phase II problem of finding an optimal solution by solving a series of Phase I feasibility problems. Strict improvement is attained at each iteration in the Phase I algorithm, and the Phase II sequence of feasibility problems has linear convergence in the number of Phase I problems. When tested on the 30 smallest NETLIB linear programming test problems, the computational results for the new Phase II algorithm were over 15% faster than the simplex method; on some problems, it was almost two times faster, and on one problem it was four times faster.
IESIP - AN IMPROVED EXPLORATORY SEARCH TECHNIQUE FOR PURE INTEGER LINEAR PROGRAMMING PROBLEMS
NASA Technical Reports Server (NTRS)
Fogle, F. R.
1994-01-01
IESIP, an Improved Exploratory Search Technique for Pure Integer Linear Programming Problems, addresses the problem of optimizing an objective function of one or more variables subject to a set of confining functions or constraints by a method called discrete optimization or integer programming. Integer programming is based on a specific form of the general linear programming problem in which all variables in the objective function and all variables in the constraints are integers. While more difficult, integer programming is required for accuracy when modeling systems with small numbers of components such as the distribution of goods, machine scheduling, and production scheduling. IESIP establishes a new methodology for solving pure integer programming problems by utilizing a modified version of the univariate exploratory move developed by Robert Hooke and T.A. Jeeves. IESIP also takes some of its technique from the greedy procedure and the idea of unit neighborhoods. A rounding scheme uses the continuous solution found by traditional methods (simplex or other suitable technique) and creates a feasible integer starting point. The Hook and Jeeves exploratory search is modified to accommodate integers and constraints and is then employed to determine an optimal integer solution from the feasible starting solution. The user-friendly IESIP allows for rapid solution of problems up to 10 variables in size (limited by DOS allocation). Sample problems compare IESIP solutions with the traditional branch-and-bound approach. IESIP is written in Borland's TURBO Pascal for IBM PC series computers and compatibles running DOS. Source code and an executable are provided. The main memory requirement for execution is 25K. This program is available on a 5.25 inch 360K MS DOS format diskette. IESIP was developed in 1990. IBM is a trademark of International Business Machines. TURBO Pascal is registered by Borland International.
Stable computation of search directions for near-degenerate linear programming problems
Hough, P.D.
1997-03-01
In this paper, we examine stability issues that arise when computing search directions ({delta}x, {delta}y, {delta} s) for a primal-dual path-following interior point method for linear programming. The dual step {delta}y can be obtained by solving a weighted least-squares problem for which the weight matrix becomes extremely il conditioned near the boundary of the feasible region. Hough and Vavisis proposed using a type of complete orthogonal decomposition (the COD algorithm) to solve such a problem and presented stability results. The work presented here addresses the stable computation of the primal step {delta}x and the change in the dual slacks {delta}s. These directions can be obtained in a straight-forward manner, but near-degeneracy in the linear programming instance introduces ill-conditioning which can cause numerical problems in this approach. Therefore, we propose a new method of computing {delta}x and {delta}s. More specifically, this paper describes and orthogonal projection algorithm that extends the COD method. Unlike other algorithms, this method is stable for interior point methods without assuming nondegeneracy in the linear programming instance. Thus, it is more general than other algorithms on near-degenerate problems.
TOPSIS approach to linear fractional bi-level MODM problem based on fuzzy goal programming
NASA Astrophysics Data System (ADS)
Dey, Partha Pratim; Pramanik, Surapati; Giri, Bibhas C.
2014-07-01
The objective of this paper is to present a technique for order preference by similarity to ideal solution (TOPSIS) algorithm to linear fractional bi-level multi-objective decision-making problem. TOPSIS is used to yield most appropriate alternative from a finite set of alternatives based upon simultaneous shortest distance from positive ideal solution (PIS) and furthest distance from negative ideal solution (NIS). In the proposed approach, first, the PIS and NIS for both levels are determined and the membership functions of distance functions from PIS and NIS of both levels are formulated. Linearization technique is used in order to transform the non-linear membership functions into equivalent linear membership functions and then normalize them. A possible relaxation on decision for both levels is considered for avoiding decision deadlock. Then fuzzy goal programming models are developed to achieve compromise solution of the problem by minimizing the negative deviational variables. Distance function is used to identify the optimal compromise solution. The paper presents a hybrid model of TOPSIS and fuzzy goal programming. An illustrative numerical example is solved to clarify the proposed approach. Finally, to demonstrate the efficiency of the proposed approach, the obtained solution is compared with the solution derived from existing methods in the literature.
Coelho, Clarimar José; Galvão, Roberto K H; de Araújo, Mário César U; Pimentel, Maria Fernanda; da Silva, Edvan Cirino
2003-01-01
A novel strategy for the optimization of wavelet transforms with respect to the statistics of the data set in multivariate calibration problems is proposed. The optimization follows a linear semi-infinite programming formulation, which does not display local maxima problems and can be reproducibly solved with modest computational effort. After the optimization, a variable selection algorithm is employed to choose a subset of wavelet coefficients with minimal collinearity. The selection allows the building of a calibration model by direct multiple linear regression on the wavelet coefficients. In an illustrative application involving the simultaneous determination of Mn, Mo, Cr, Ni, and Fe in steel samples by ICP-AES, the proposed strategy yielded more accurate predictions than PCR, PLS, and nonoptimized wavelet regression. PMID:12767151
Takabe, Satoshi; Hukushima, Koji
2016-05-01
Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α=2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c=e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c=1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α≥3, minimum vertex covers on α-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c=e/(α-1) where the replica symmetry is broken. PMID:27301006
NASA Astrophysics Data System (ADS)
Takabe, Satoshi; Hukushima, Koji
2016-05-01
Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α -uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α =2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c =e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c =1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α ≥3 , minimum vertex covers on α -uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c =e /(α -1 ) where the replica symmetry is broken.
An improved exploratory search technique for pure integer linear programming problems
NASA Technical Reports Server (NTRS)
Fogle, F. R.
1990-01-01
The development is documented of a heuristic method for the solution of pure integer linear programming problems. The procedure draws its methodology from the ideas of Hooke and Jeeves type 1 and 2 exploratory searches, greedy procedures, and neighborhood searches. It uses an efficient rounding method to obtain its first feasible integer point from the optimal continuous solution obtained via the simplex method. Since this method is based entirely on simple addition or subtraction of one to each variable of a point in n-space and the subsequent comparison of candidate solutions to a given set of constraints, it facilitates significant complexity improvements over existing techniques. It also obtains the same optimal solution found by the branch-and-bound technique in 44 of 45 small to moderate size test problems. Two example problems are worked in detail to show the inner workings of the method. Furthermore, using an established weighted scheme for comparing computational effort involved in an algorithm, a comparison of this algorithm is made to the more established and rigorous branch-and-bound method. A computer implementation of the procedure, in PC compatible Pascal, is also presented and discussed.
A Mixed Integer Linear Program for Solving a Multiple Route Taxi Scheduling Problem
NASA Technical Reports Server (NTRS)
Montoya, Justin Vincent; Wood, Zachary Paul; Rathinam, Sivakumar; Malik, Waqar Ahmad
2010-01-01
Aircraft movements on taxiways at busy airports often create bottlenecks. This paper introduces a mixed integer linear program to solve a Multiple Route Aircraft Taxi Scheduling Problem. The outputs of the model are in the form of optimal taxi schedules, which include routing decisions for taxiing aircraft. The model extends an existing single route formulation to include routing decisions. An efficient comparison framework compares the multi-route formulation and the single route formulation. The multi-route model is exercised for east side airport surface traffic at Dallas/Fort Worth International Airport to determine if any arrival taxi time savings can be achieved by allowing arrivals to have two taxi routes: a route that crosses an active departure runway and a perimeter route that avoids the crossing. Results indicate that the multi-route formulation yields reduced arrival taxi times over the single route formulation only when a perimeter taxiway is used. In conditions where the departure aircraft are given an optimal and fixed takeoff sequence, accumulative arrival taxi time savings in the multi-route formulation can be as high as 3.6 hours more than the single route formulation. If the departure sequence is not optimal, the multi-route formulation results in less taxi time savings made over the single route formulation, but the average arrival taxi time is significantly decreased.
NASA Technical Reports Server (NTRS)
Young, Katherine C.; Sobieszczanski-Sobieski, Jaroslaw
1988-01-01
This project has two objectives. The first is to determine whether linear programming techniques can improve performance when handling design optimization problems with a large number of design variables and constraints relative to the feasible directions algorithm. The second purpose is to determine whether using the Kreisselmeier-Steinhauser (KS) function to replace the constraints with one constraint will reduce the cost of total optimization. Comparisons are made using solutions obtained with linear and non-linear methods. The results indicate that there is no cost saving using the linear method or in using the KS function to replace constraints.
Sparse linear programming subprogram
Hanson, R.J.; Hiebert, K.L.
1981-12-01
This report describes a subprogram, SPLP(), for solving linear programming problems. The package of subprogram units comprising SPLP() is written in Fortran 77. The subprogram SPLP() is intended for problems involving at most a few thousand constraints and variables. The subprograms are written to take advantage of sparsity in the constraint matrix. A very general problem statement is accepted by SPLP(). It allows upper, lower, or no bounds on the variables. Both the primal and dual solutions are returned as output parameters. The package has many optional features. Among them is the ability to save partial results and then use them to continue the computation at a later time.
NASA Technical Reports Server (NTRS)
Ferencz, Donald C.; Viterna, Larry A.
1991-01-01
ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.
Linear Programming across the Curriculum
ERIC Educational Resources Information Center
Yoder, S. Elizabeth; Kurz, M. Elizabeth
2015-01-01
Linear programming (LP) is taught in different departments across college campuses with engineering and management curricula. Modeling an LP problem is taught in every linear programming class. As faculty teaching in Engineering and Management departments, the depth to which teachers should expect students to master this particular type of…
NASA Astrophysics Data System (ADS)
Noor-E-Alam, Md.; Doucette, John
2015-08-01
Grid-based location problems (GBLPs) can be used to solve location problems in business, engineering, resource exploitation, and even in the field of medical sciences. To solve these decision problems, an integer linear programming (ILP) model is designed and developed to provide the optimal solution for GBLPs considering fixed cost criteria. Preliminary results show that the ILP model is efficient in solving small to moderate-sized problems. However, this ILP model becomes intractable in solving large-scale instances. Therefore, a decomposition heuristic is proposed to solve these large-scale GBLPs, which demonstrates significant reduction of solution runtimes. To benchmark the proposed heuristic, results are compared with the exact solution via ILP. The experimental results show that the proposed method significantly outperforms the exact method in runtime with minimal (and in most cases, no) loss of optimality.
NASA Technical Reports Server (NTRS)
Utku, S.
1969-01-01
A general purpose digital computer program for the in-core solution of linear equilibrium problems of structural mechanics is documented. The program requires minimum input for the description of the problem. The solution is obtained by means of the displacement method and the finite element technique. Almost any geometry and structure may be handled because of the availability of linear, triangular, quadrilateral, tetrahedral, hexahedral, conical, triangular torus, and quadrilateral torus elements. The assumption of piecewise linear deflection distribution insures monotonic convergence of the deflections from the stiffer side with decreasing mesh size. The stresses are provided by the best-fit strain tensors in the least squares at the mesh points where the deflections are given. The selection of local coordinate systems whenever necessary is automatic. The core memory is used by means of dynamic memory allocation, an optional mesh-point relabelling scheme and imposition of the boundary conditions during the assembly time.
NASA Technical Reports Server (NTRS)
Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.
1982-01-01
The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.
The linear separability problem: some testing methods.
Elizondo, D
2006-03-01
The notion of linear separability is used widely in machine learning research. Learning algorithms that use this concept to learn include neural networks (single layer perceptron and recursive deterministic perceptron), and kernel machines (support vector machines). This paper presents an overview of several of the methods for testing linear separability between two classes. The methods are divided into four groups: Those based on linear programming, those based on computational geometry, one based on neural networks, and one based on quadratic programming. The Fisher linear discriminant method is also presented. A section on the quantification of the complexity of classification problems is included. PMID:16566462
ERIC Educational Resources Information Center
Nakhanu, Shikuku Beatrice; Musasia, Amadalo Maurice
2015-01-01
The topic Linear Programming is included in the compulsory Kenyan secondary school mathematics curriculum at form four. The topic provides skills for determining best outcomes in a given mathematical model involving some linear relationship. This technique has found application in business, economics as well as various engineering fields. Yet many…
NASA Astrophysics Data System (ADS)
Skerget, P.; Brebbia, C. A.
In many practical applications of boundary elements, the potential problems may be nonlinear. The use of Kirchoff's transform provides an approach to convert a nonlinear material problem into a linear one. A description of several different shape functions to define the conductivity is presented. Attention is given to the type of integral equations which are obtained if the Kirchoff's transform is applied for nonlinear material in the presence of mixed boundary conditions. The integral formulation for nonlinear radiation boundary conditions with and without potential dependent conductivity is also considered. For steady heat conduction problems with constant conductivity a boundary integral equation relating boundary values for temperatures (or potentials) and its normal derivatives over the boundary can be obtained. Applications which concern the solution of steady state conduction problems are investigated. The problems are related to a hollow cylinder, a nuclear reactor pressure vessel, and an industrial furnace.
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.
Linearization problem in pseudolite surveys
NASA Astrophysics Data System (ADS)
Cellmer, Slawomir; Rapinski, Jacek
2010-06-01
GPS augmented with pseudolites (PL), can be used in various engineering surveys. Also pseudolite—only navigation system can be designed and used in any place, even if GPS signal is not available (Kee et al. Development of indoor navigation system using asynchronous pseudolites, 1038-1045, 2000). Especially in engineering surveys, where harsh survey environment is common, pseudolites have a lot of applications. Pseudolites may be used in construction sites, open pit mines, city canyons, GPS and PL baseline processing is similar, although there are few differences that must be taken into account. One of the major issues is linearization problem. The source of the problem is neglecting second terms of Taylor series expansion in GPS baseline processing software. This problem occurs when the pseudolite is relatively close to the receiver, which is the case in PL surveys. In this paper authors presents the algorithm for GPS + PL data processing including, neglected in classical GPS only approach, second terms of Taylor series expansion. The mathematical model of adjustment problem, detailed proposal of application in baseline processing algorithms, and numerical tests are presented.
NASA Technical Reports Server (NTRS)
Klumpp, A. R.; Lawson, C. L.
1988-01-01
Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.
Long term fuel scheduling linear programming
Asgarpoor, S. . Dept. of Electrical Engineering); Gul, N. )
1992-01-01
This paper presents an application of linear programming (LP) revised simplex method in order to solve the fuel scheduling problem. A regression method is applied to determine the polynomial cost curves, and a separable programming technique is used to linearize the objective function and the constraints for LP application. Results based on sample data obtained from Omaha Public Power District (OPPD) are presented to demonstrate the LP application to this problem.
ALPS - A LINEAR PROGRAM SOLVER
NASA Technical Reports Server (NTRS)
Viterna, L. A.
1994-01-01
Linear programming is a widely-used engineering and management tool. Scheduling, resource allocation, and production planning are all well-known applications of linear programs (LP's). Most LP's are too large to be solved by hand, so over the decades many computer codes for solving LP's have been developed. ALPS, A Linear Program Solver, is a full-featured LP analysis program. ALPS can solve plain linear programs as well as more complicated mixed integer and pure integer programs. ALPS also contains an efficient solution technique for pure binary (0-1 integer) programs. One of the many weaknesses of LP solvers is the lack of interaction with the user. ALPS is a menu-driven program with no special commands or keywords to learn. In addition, ALPS contains a full-screen editor to enter and maintain the LP formulation. These formulations can be written to and read from plain ASCII files for portability. For those less experienced in LP formulation, ALPS contains a problem "parser" which checks the formulation for errors. ALPS creates fully formatted, readable reports that can be sent to a printer or output file. ALPS is written entirely in IBM's APL2/PC product, Version 1.01. The APL2 workspace containing all the ALPS code can be run on any APL2/PC system (AT or 386). On a 32-bit system, this configuration can take advantage of all extended memory. The user can also examine and modify the ALPS code. The APL2 workspace has also been "packed" to be run on any DOS system (without APL2) as a stand-alone "EXE" file, but has limited memory capacity on a 640K system. A numeric coprocessor (80X87) is optional but recommended. The standard distribution medium for ALPS is a 5.25 inch 360K MS-DOS format diskette. IBM, IBM PC and IBM APL2 are registered trademarks of International Business Machines Corporation. MS-DOS is a registered trademark of Microsoft Corporation.
Gadgets, approximation, and linear programming
Trevisan, L.; Sudan, M.; Sorkin, G.B.; Williamson, D.P.
1996-12-31
We present a linear-programming based method for finding {open_quotes}gadgets{close_quotes}, i.e., combinatorial structures reducing constraints of one optimization problems to constraints of another. A key step in this method is a simple observation which limits the search space to a finite one. Using this new method we present a number of new, computer-constructed gadgets for several different reductions. This method also answers a question posed by on how to prove the optimality of gadgets-we show how LP duality gives such proofs. The new gadgets improve hardness results for MAX CUT and MAX DICUT, showing that approximating these problems to within factors of 60/61 and 44/45 respectively is N P-hard. We also use the gadgets to obtain an improved approximation algorithm for MAX 3SAT which guarantees an approximation ratio of .801. This improves upon the previous best bound of .7704.
Generalised Assignment Matrix Methodology in Linear Programming
ERIC Educational Resources Information Center
Jerome, Lawrence
2012-01-01
Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…
The Vertical Linear Fractional Initialization Problem
NASA Technical Reports Server (NTRS)
Lorenzo, Carl F.; Hartley, Tom T.
1999-01-01
This paper presents a solution to the initialization problem for a system of linear fractional-order differential equations. The scalar problem is considered first, and solutions are obtained both generally and for a specific initialization. Next the vector fractional order differential equation is considered. In this case, the solution is obtained in the form of matrix F-functions. Some control implications of the vector case are discussed. The suggested method of problem solution is shown via an example.
Singular linear-quadratic control problem for systems with linear delay
Sesekin, A. N.
2013-12-18
A singular linear-quadratic optimization problem on the trajectories of non-autonomous linear differential equations with linear delay is considered. The peculiarity of this problem is the fact that this problem has no solution in the class of integrable controls. To ensure the existence of solutions is required to expand the class of controls including controls with impulse components. Dynamical systems with linear delay are used to describe the motion of pantograph from the current collector with electric traction, biology, etc. It should be noted that for practical problems fact singularity criterion of quality is quite commonly occurring, and therefore the study of these problems is surely important. For the problem under discussion optimal programming control contained impulse components at the initial and final moments of time is constructed under certain assumptions on the functional and the right side of the control system.
Random generation of structured linear optimization problems
Arthur, J.; Frendewey, J. Jr.
1994-12-31
We describe the on-going development of a random generator for linear optimization problems (LPs) founded on the concept of block structure. The general LP: minimize z = cx subject to Ax = b, x {ge} 0 can take a variety of special forms determined (primarily) by predefined structures on the matrix A of constraint coefficients. The authors have developed several random problem generators which provide instances of LPs having such structure; in particular (i) general (non-structured) problems, (ii) generalized upper bound (GUB) constraints, (iii) minimum cost network flow problems, (iv) transportation and assignment problems, (v) shortest path problems, (vi) generalized network flow problems, and (vii) multicommodity network flow problems. This paper discusses the general philosophy behind the construction of these generators. In addition, the task of combining the generators into a single generator -- in which the matrix A can contain various blocks, each of a prescribed structure from those mentioned above -- is described.
Piecewise linear approximation for hereditary control problems
NASA Technical Reports Server (NTRS)
Propst, Georg
1990-01-01
This paper presents finite-dimensional approximations for linear retarded functional differential equations by use of discontinuous piecewise linear functions. The approximation scheme is applied to optimal control problems, when a quadratic cost integral must be minimized subject to the controlled retarded system. It is shown that the approximate optimal feedback operators converge to the true ones both in the case where the cost integral ranges over a finite time interval, as well as in the case where it ranges over an infinite time interval. The arguments in the last case rely on the fact that the piecewise linear approximations to stable systems are stable in a uniform sense.
Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel
ERIC Educational Resources Information Center
El-Gebeily, M.; Yushau, B.
2008-01-01
In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…
Linear programming computational experience with onyx
Atrek, E.
1994-12-31
ONYX is a linear programming software package based on an efficient variation of the gradient projection method. When fully configured, it is intended for application to industrial size problems. While the computational experience is limited at the time of this abstract, the technique is found to be robust and competitive with existing methodology in terms of both accuracy and speed. An overview of the approach is presented together with a description of program capabilities, followed by a discussion of up-to-date computational experience with the program. Conclusions include advantages of the approach and envisioned future developments.
Numerical linear algebra for reconstruction inverse problems
NASA Astrophysics Data System (ADS)
Nachaoui, Abdeljalil
2004-01-01
Our goal in this paper is to discuss various issues we have encountered in trying to find and implement efficient solvers for a boundary integral equation (BIE) formulation of an iterative method for solving a reconstruction problem. We survey some methods from numerical linear algebra, which are relevant for the solution of this class of inverse problems. We motivate the use of our constructing algorithm, discuss its implementation and mention the use of preconditioned Krylov methods.
The linear regulator problem for parabolic systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Kunisch, K.
1983-01-01
An approximation framework is presented for computation (in finite imensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is shown how these results may be used in the linear optimal regulator problem for a large class of parabolic systems.
A program for identification of linear systems
NASA Technical Reports Server (NTRS)
Buell, J.; Kalaba, R.; Ruspini, E.; Yakush, A.
1971-01-01
A program has been written for the identification of parameters in certain linear systems. These systems appear in biomedical problems, particularly in compartmental models of pharmacokinetics. The method presented here assumes that some of the state variables are regularly modified by jump conditions. This simulates administration of drugs following some prescribed drug regime. Parameters are identified by a least-square fit of the linear differential system to a set of experimental observations. The method is especially suited when the interval of observation of the system is very long.
Successive linear optimization approach to the dynamic traffic assignment problem
Ho, J.K.
1980-11-01
A dynamic model for the optimal control of traffic flow over a network is considered. The model, which treats congestion explicitly in the flow equations, gives rise to nonlinear, nonconvex mathematical programming problems. It has been shown for a piecewise linear version of this model that a global optimum is contained in the set of optimal solutions of a certain linear program. A sufficient condition for optimality which implies that a global optimum can be obtained by successively optimizing at most N + 1 objective functions for the linear program, where N is the number of time periods in the planning horizon is presented. Computational results are reported to indicate the efficiency of this approach.
A path-following interior-point algorithm for linear and quadratic problems
Wright, S.J.
1993-12-01
We describe an algorithm for the monotone linear complementarity problem that converges for many positive, not necessarily feasible, starting point and exhibits polynomial complexity if some additional assumptions are made on the starting point. If the problem has a strictly complementary solution, the method converges subquadratically. We show that the algorithm and its convergence extend readily to the mixed monotone linear complementarity problem and, hence, to all the usual formulations of the linear programming and convex quadratic programming problems.
Numerical stability in problems of linear algebra.
NASA Technical Reports Server (NTRS)
Babuska, I.
1972-01-01
Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.
Computer Program For Linear Algebra
NASA Technical Reports Server (NTRS)
Krogh, F. T.; Hanson, R. J.
1987-01-01
Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.
Investigating Integer Restrictions in Linear Programming
ERIC Educational Resources Information Center
Edwards, Thomas G.; Chelst, Kenneth R.; Principato, Angela M.; Wilhelm, Thad L.
2015-01-01
Linear programming (LP) is an application of graphing linear systems that appears in many Algebra 2 textbooks. Although not explicitly mentioned in the Common Core State Standards for Mathematics, linear programming blends seamlessly into modeling with mathematics, the fourth Standard for Mathematical Practice (CCSSI 2010, p. 7). In solving a…
Strengthening Programs through Problem Solving.
ERIC Educational Resources Information Center
Dyer, Jim
1993-01-01
Describes a secondary agricultural education program that was a dumping ground for academically disadvantaged students. Discusses how such a program can be improved by identifying problems and symptoms, treating problems, and goal setting. (JOW)
Multiobjective power dispatch using fuzzy linear programming
Yang, H.T.; Huang, C.M.; Lee, H.M.; Huang, C.L.
1995-12-31
This paper presents a new fuzzy linear programming (FLP) approach to determine the multiobjective power dispatch problem by taking into account fuel cost and environmental impact of NO{sub x} emission. The FLP technique first separately optimizes each objective. To further offer the best compromise solution out of the non-inferiority domain obtained by the FLP based operator, a preference index of distance membership function is used to aid the power system operator to adjust the generation levels in a most economic manner but also with minimal impact on the environments. The effectiveness of the proposed approach has been demonstrated on a 10-bus 5-generator system. Numerical results reveal that the FLP is a promising and efficient approach for dealing with the multiobjective nature of power dispatch problem.
Comparison of open-source linear programming solvers.
Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin D.; Jones, Katherine A.; Martin, Nathaniel; Detry, Richard Joseph
2013-10-01
When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.
Convergence of linear programming using a Hopfield net
Lu, Shin-yee; Berryman, J.G.
1990-11-01
Hopfield nets are interconnected networks of simple analog Processors. Such networks have been applied to a variety of optimization problems including linear programming problems. We revised the energy function used in a Hopfield net such that the network can be implemented on a digital computer to solve linearing programming problems. We also proved that the revised discrete Hopfield net coverages, and gave the conditions of convergence. The approach is tested on two large and sparse linear programming problems. In both cases we could not reach the optimal solutions, but solutions with 1% error can be attained in less than 3 minutes of CPU time on a SUN SPARC station. The optimal solutions can be obtained by the simplex method, but required five times more CPU time. 10 refs., 1 tab.
Boolean approach to zero-one linear programming
Hulme, B.L.; Baca, L.S.
1984-07-01
Problems of minimizing or maximizing a linear objective function in zero-one variables subject to linear constraints can be solved by Boolean algebraic methods. This report gives both a general procedure for stating such problems in Boolean form and a solution procedure that has been implemented by a SETS user program. The program uses the Boolean algebraic formula manipulation techniques of the SETS language. Sample problems illustrate how to make optimum choices in the contexts of physical protection, packing knapsacks, designing manufacturing processes and making assignments.
Hybrid evolutionary programming for heavily constrained problems.
Myung, H; Kim, J H
1996-01-01
A hybrid of evolutionary programming (EP) and a deterministic optimization procedure is applied to a series of non-linear and quadratic optimization problems. The hybrid scheme is compared with other existing schemes such as EP alone, two-phase (TP) optimization, and EP with a non-stationary penalty function (NS-EP). The results indicate that the hybrid method can outperform the other methods when addressing heavily constrained optimization problems in terms of computational efficiency and solution accuracy. PMID:8833746
Breadboard linear array scan imager program
NASA Technical Reports Server (NTRS)
1975-01-01
The performance was evaluated of large scale integration photodiode arrays in a linear array scan imaging system breadboard for application to multispectral remote sensing of the earth's resources. Objectives, approach, implementation, and test results of the program are presented.
From Parity and Payoff Games to Linear Programming
NASA Astrophysics Data System (ADS)
Schewe, Sven
This paper establishes a surprising reduction from parity and mean payoff games to linear programming problems. While such a connection is trivial for solitary games, it is surprising for two player games, because the players have opposing objectives, whose natural translations into an optimisation problem are minimisation and maximisation, respectively. Our reduction to linear programming circumvents the need for concurrent minimisation and maximisation by replacing one of them, the maximisation, by approximation. The resulting optimisation problem can be translated to a linear programme by a simple space transformation, which is inexpensive in the unit cost model, but results in an exponential growth of the coefficients. The discovered connection opens up unexpected applications - like μ-calculus model checking - of linear programming in the unit cost model, and thus turns the intriguing academic problem of finding a polynomial time algorithm for linear programming in this model of computation (and subsequently a strongly polynomial algorithm) into a problem of paramount practical importance: All advancements in this area can immediately be applied to accelerate solving parity and payoff games, or to improve their complexity analysis.
A multistage linear array assignment problem
NASA Technical Reports Server (NTRS)
Nicol, David M.; Shier, D. R.; Kincaid, R. K.; Richards, D. S.
1988-01-01
The implementation of certain algorithms on parallel processing computing architectures can involve partitioning contiguous elements into a fixed number of groups, each of which is to be handled by a single processor. It is desired to find an assignment of elements to processors that minimizes the sum of the maximum workloads experienced at each stage. This problem can be viewed as a multi-objective network optimization problem. Polynomially-bounded algorithms are developed for the case of two stages, whereas the associated decision problem (for an arbitrary number of stages) is shown to be NP-complete. Heuristic procedures are therefore proposed and analyzed for the general problem. Computational experience with one of the exact problems, incorporating certain pruning rules, is presented with one of the exact problems. Empirical results also demonstrate that one of the heuristic procedures is especially effective in practice.
Solution of the linear regression problem using matrix correction methods in the l 1 metric
NASA Astrophysics Data System (ADS)
Gorelik, V. A.; Trembacheva (Barkalova), O. S.
2016-02-01
The linear regression problem is considered as an improper interpolation problem. The metric l 1 is used to correct (approximate) all the initial data. A probabilistic justification of this metric in the case of the exponential noise distribution is given. The original improper interpolation problem is reduced to a set of a finite number of linear programming problems. The corresponding computational algorithms are implemented in MATLAB.
An amoeboid algorithm for solving linear transportation problem
NASA Astrophysics Data System (ADS)
Gao, Cai; Yan, Chao; Zhang, Zili; Hu, Yong; Mahadevan, Sankaran; Deng, Yong
2014-03-01
Transportation Problem (TP) is one of the basic operational research problems, which plays an important role in many practical applications. In this paper, a bio-inspired mathematical model is proposed to handle the Linear Transportation Problem (LTP) in directed networks by modifying the original amoeba model Physarum Solver. Several examples are used to prove that the provided model can effectively solve Balanced Transportation Problem (BTP), Unbalanced Transportation Problem (UTP), especially the Generalized Transportation Problem (GTP), in a nondiscrete way.
Technology Transfer Automated Retrieval System (TEKTRAN)
A stochastic/linear program Excel workbook was developed consisting of two worksheets illustrating linear and stochastic program approaches. Both approaches used the Excel Solver add-in. A published linear program problem served as an example for the ingredients, nutrients and costs and as a benchma...
Optimized remedial groundwater extraction using linear programming
Quinn, J.J.
1995-12-31
Groundwater extraction systems are typically installed to remediate contaminant plumes or prevent further spread of contamination. These systems are expensive to install and maintain. A traditional approach to designing such a wellfield uses a series of trial-and-error simulations to test the effects of various well locations and pump rates. However, the optimal locations and pump rates of extraction wells are difficult to determine when objectives related to the site hydrogeology and potential pumping scheme are considered. This paper describes a case study of an application of linear programming theory to determine optimal well placement and pump rates. The objectives of the pumping scheme were to contain contaminant migration and reduce contaminant concentrations while minimizing the total amount of water pumped and treated. Past site activities at the area under study included disposal of contaminants in pits. Several groundwater plumes have been identified, and others may be present. The area of concern is bordered on three sides by a wetland, which receives a portion of its input budget as groundwater discharge from the pits. Optimization of the containment pumping scheme was intended to meet three goals: (1) prevent discharge of contaminated groundwater to the wetland, (2) minimize the total water pumped and treated (cost benefit), and (3) avoid dewatering of the wetland (cost and ecological benefits). Possible well locations were placed at known source areas. To constrain the problem, the optimization program was instructed to prevent any flow toward the wetland along a user-specified border. In this manner, the optimization routine selects well locations and pump rates so that a groundwater divide is produced along this boundary.
Planning under uncertainty solving large-scale stochastic linear programs
Infanger, G. . Dept. of Operations Research Technische Univ., Vienna . Inst. fuer Energiewirtschaft)
1992-12-01
For many practical problems, solutions obtained from deterministic models are unsatisfactory because they fail to hedge against certain contingencies that may occur in the future. Stochastic models address this shortcoming, but up to recently seemed to be intractable due to their size. Recent advances both in solution algorithms and in computer technology now allow us to solve important and general classes of practical stochastic problems. We show how large-scale stochastic linear programs can be efficiently solved by combining classical decomposition and Monte Carlo (importance) sampling techniques. We discuss the methodology for solving two-stage stochastic linear programs with recourse, present numerical results of large problems with numerous stochastic parameters, show how to efficiently implement the methodology on a parallel multi-computer and derive the theory for solving a general class of multi-stage problems with dependency of the stochastic parameters within a stage and between different stages.
Sparse Substring Pattern Set Discovery Using Linear Programming Boosting
NASA Astrophysics Data System (ADS)
Kashihara, Kazuaki; Hatano, Kohei; Bannai, Hideo; Takeda, Masayuki
In this paper, we consider finding a small set of substring patterns which classifies the given documents well. We formulate the problem as 1 norm soft margin optimization problem where each dimension corresponds to a substring pattern. Then we solve this problem by using LPBoost and an optimal substring discovery algorithm. Since the problem is a linear program, the resulting solution is likely to be sparse, which is useful for feature selection. We evaluate the proposed method for real data such as movie reviews.
Spline smoothing of histograms by linear programming
NASA Technical Reports Server (NTRS)
Bennett, J. O.
1972-01-01
An algorithm for an approximating function to the frequency distribution is obtained from a sample of size n. To obtain the approximating function a histogram is made from the data. Next, Euclidean space approximations to the graph of the histogram using central B-splines as basis elements are obtained by linear programming. The approximating function has area one and is nonnegative.
Synthesizing Dynamic Programming Algorithms from Linear Temporal Logic Formulae
NASA Technical Reports Server (NTRS)
Rosu, Grigore; Havelund, Klaus
2001-01-01
The problem of testing a linear temporal logic (LTL) formula on a finite execution trace of events, generated by an executing program, occurs naturally in runtime analysis of software. We present an algorithm which takes an LTL formula and generates an efficient dynamic programming algorithm. The generated algorithm tests whether the LTL formula is satisfied by a finite trace of events given as input. The generated algorithm runs in linear time, its constant depending on the size of the LTL formula. The memory needed is constant, also depending on the size of the formula.
Train Repathing in Emergencies Based on Fuzzy Linear Programming
Cui, Bingmou
2014-01-01
Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model) to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm. PMID:25121128
Train repathing in emergencies based on fuzzy linear programming.
Meng, Xuelei; Cui, Bingmou
2014-01-01
Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model) to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm. PMID:25121128
Breathing Problems: An Individualized Program.
ERIC Educational Resources Information Center
Vodola, Thomas M.
As one of the components of the Project ACTIVE (All Children Totally Involved Exercising) Teacher Training Model Kit, the manual is designed to enable the educator to organize, conduct, and evaluate individualized-personalized physical education programs for children (prekindergarten through high school) with breathing problems. An introductory…
Multisplitting for linear, least squares and nonlinear problems
Renaut, R.
1996-12-31
In earlier work, presented at the 1994 Iterative Methods meeting, a multisplitting (MS) method of block relaxation type was utilized for the solution of the least squares problem, and nonlinear unconstrained problems. This talk will focus on recent developments of the general approach and represents joint work both with Andreas Frommer, University of Wupertal for the linear problems and with Hans Mittelmann, Arizona State University for the nonlinear problems.
Experiences with linear solvers for oil reservoir simulation problems
Joubert, W.; Janardhan, R.; Biswas, D.; Carey, G.
1996-12-31
This talk will focus on practical experiences with iterative linear solver algorithms used in conjunction with Amoco Production Company`s Falcon oil reservoir simulation code. The goal of this study is to determine the best linear solver algorithms for these types of problems. The results of numerical experiments will be presented.
Inverse Modelling Problems in Linear Algebra Undergraduate Courses
ERIC Educational Resources Information Center
Martinez-Luaces, Victor E.
2013-01-01
This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…
Linear Programming Problems for Generalized Uncertainty
ERIC Educational Resources Information Center
Thipwiwatpotjana, Phantipa
2010-01-01
Uncertainty occurs when there is more than one realization that can represent an information. This dissertation concerns merely discrete realizations of an uncertainty. Different interpretations of an uncertainty and their relationships are addressed when the uncertainty is not a probability of each realization. A well known model that can handle…
Transmission network planning using linear programming
Villasana, R.; Garver, L.L.; Salon, S.J.
1985-02-01
In long range transmission planning, where new load growth, new generation sites and perhaps a new voltage level are to be considered, a computer aided method of visualizing new circuits in a network context is needed. The new method presented meets this need by the combined use of a linear (dc) power flow transmission model and a transportation model (also known as a trans-shipment model). The dc transmission model is solved for the facilities network by obeying both of Kirchhoff's laws, flow conservation at each bus and voltage conservation around each loop. The transportation model is solved for the overloads by obeying only the bus flow conservation law while minimizing a cost objective function. The linear programming solution of the two models together identifies where capacity shortages exist, where to add new circuits, and how much new capacity is needed. A standard linear programming computer package is used to solve the two model formulation. The overload network model is only a mathematical assistance in selecting new lines and is completely unused when the network design is complete and contains no overloads. An application of the model to the horizon-year planning of a six bus network serves to illustrate the method.
Controller design approach based on linear programming.
Tanaka, Ryo; Shibasaki, Hiroki; Ogawa, Hiromitsu; Murakami, Takahiro; Ishida, Yoshihisa
2013-11-01
This study explains and demonstrates the design method for a control system with a load disturbance observer. Observer gains are determined by linear programming (LP) in terms of the Routh-Hurwitz stability criterion and the final-value theorem. In addition, the control model has a feedback structure, and feedback gains are determined to be the linear quadratic regulator. The simulation results confirmed that compared with the conventional method, the output estimated by our proposed method converges to a reference input faster when a load disturbance is added to a control system. In addition, we also confirmed the effectiveness of the proposed method by performing an experiment with a DC motor. PMID:23910155
Voila: A visual object-oriented iterative linear algebra problem solving environment
Edwards, H.C.; Hayes, L.J.
1994-12-31
Application of iterative methods to solve a large linear system of equations currently involves writing a program which calls iterative method subprograms from a large software package. These subprograms have complex interfaces which are difficult to use and even more difficult to program. A problem solving environment specifically tailored to the development and application of iterative methods is needed. This need will be fulfilled by Voila, a problem solving environment which provides a visual programming interface to object-oriented iterative linear algebra kernels. Voila will provide several quantum improvements over current iterative method problem solving environments. First, programming and applying iterative methods is considerably simplified through Voila`s visual programming interface. Second, iterative method algorithm implementations are independent of any particular sparse matrix data structure through Voila`s object-oriented kernels. Third, the compile-link-debug process is eliminated as Voila operates as an interpreter.
Fuzzy Linear Programming and its Application in Home Textile Firm
NASA Astrophysics Data System (ADS)
Vasant, P.; Ganesan, T.; Elamvazuthi, I.
2011-06-01
In this paper, new fuzzy linear programming (FLP) based methodology using a specific membership function, named as modified logistic membership function is proposed. The modified logistic membership function is first formulated and its flexibility in taking up vagueness in parameter is established by an analytical approach. The developed methodology of FLP has provided a confidence in applying to real life industrial production planning problem. This approach of solving industrial production planning problem can have feedback with the decision maker, the implementer and the analyst.
Optimized groundwater containment using linear programming
Quinn, J.J.; Johnson, R.L.; Durham, L.A.
1998-07-01
Groundwater extraction systems are typically installed to contain contaminant plumes. These systems are expensive to install and maintain. A traditional approach to designing such a wellfield is to use a series of trial-and-error simulations to test the effects of various well locations and pump rates. However, optimal locations and pump rates of extraction wells are difficult to determine when the objectives of the potential pumping scheme and the site hydrogeology are considered. This paper describes a case study of an application of linear programming theory to determine optimal well placement and pump rates. Calculations were conducted by using ModMan to link a calibrated MODFLOW flow model with LINDO, a linear programming package. Past activities at the site under study included disposal of contaminants in pits. Several groundwater plumes have been identified, and others may be present. The area of concern is bordered on three sides by a wetland, which receives a portion of its input water budget as groundwater discharge from the disposal area. The objective function of the optimization was to minimize the rate of groundwater extraction while preventing discharge to the marsh across a user-specified boundary. In this manner, the optimization routine selects well locations and pump rates to produce a groundwater divide along this boundary.
Finding Optimal Gains In Linear-Quadratic Control Problems
NASA Technical Reports Server (NTRS)
Milman, Mark H.; Scheid, Robert E., Jr.
1990-01-01
Analytical method based on Volterra factorization leads to new approximations for optimal control gains in finite-time linear-quadratic control problem of system having infinite number of dimensions. Circumvents need to analyze and solve Riccati equations and provides more transparent connection between dynamics of system and optimal gain.
User's manual for LINEAR, a FORTRAN program to derive linear aircraft models
NASA Technical Reports Server (NTRS)
Duke, Eugene L.; Patterson, Brian P.; Antoniewicz, Robert F.
1987-01-01
This report documents a FORTRAN program that provides a powerful and flexible tool for the linearization of aircraft models. The program LINEAR numerically determines a linear system model using nonlinear equations of motion and a user-supplied nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model.
Towards an ideal preconditioner for linearized Navier-Stokes problems
Murphy, M.F.
1996-12-31
Discretizing certain linearizations of the steady-state Navier-Stokes equations gives rise to nonsymmetric linear systems with indefinite symmetric part. We show that for such systems there exists a block diagonal preconditioner which gives convergence in three GMRES steps, independent of the mesh size and viscosity parameter (Reynolds number). While this {open_quotes}ideal{close_quotes} preconditioner is too expensive to be used in practice, it provides a useful insight into the problem. We then consider various approximations to the ideal preconditioner, and describe the eigenvalues of the preconditioned systems. Finally, we compare these preconditioners numerically, and present our conclusions.
Regularized total least squares approach for nonconvolutional linear inverse problems.
Zhu, W; Wang, Y; Galatsanos, N P; Zhang, J
1999-01-01
In this correspondence, a solution is developed for the regularized total least squares (RTLS) estimate in linear inverse problems where the linear operator is nonconvolutional. Our approach is based on a Rayleigh quotient (RQ) formulation of the TLS problem, and we accomplish regularization by modifying the RQ function to enforce a smooth solution. A conjugate gradient algorithm is used to minimize the modified RQ function. As an example, the proposed approach has been applied to the perturbation equation encountered in optical tomography. Simulation results show that this method provides more stable and accurate solutions than the regularized least squares and a previously reported total least squares approach, also based on the RQ formulation. PMID:18267442
Measurement problem in PROGRAM UNIVERSE
Noyes, H.P.; Gefwert, C.
1984-12-01
We present a discrete theory that meets the measurement problem in a new way. We generate a growing universe of bit strings, labeled by 2/sup 127/ + 136 strings organized by some representation of the closed, four level, combinatorial hierarchy, of bit-length N/sub 139/ greater than or equal to 139. The rest of the strings for each label, which grow in both length and number, are called addresses. The generating algorithm, called PROGRAM UNIVERSE, starts from a random choice between the two symbols ''0'' and ''1'' and grows (a) by discriminating between two randomly chosen strings and adjoining a novel result to the universe, or when the string so generated is not novel, by (b) adjoining a randomly chosen bit at the growing end of each string. We obtain, by appropriate definitions and interpretations, stable ''particles'' which satisfy the usual relativistic kinematics and quantized angular momentum without being localizable in a continuum space-time. The labeling scheme is congruent with the ''standard model'' of quarks and leptons with three generations, but for the problem at hand, the implementation of this aspect of the theory is unimportant. What matters most is that (a) these complicated ''particles'' have the periodicities familiar from relativistic ''deBroglie waves'' and resolve in a discrete way the ''wave-particle dualism'' and (b) can be ''touched'' by our discrete equivalent of ''soft photons'' in such a way as to follow, macroscopically, the usual Rutherford scattering trajectories with the associated bound states. Thus our theory could provide a discrete description of ''measurement'' in a way that allows no conceptual barrier between the ''micro'' and the ''macro'' worlds, if we are willing to base our physics on counting and exclude the ambiguities associated with the unobservable ''continuum''. 27 refs.
An analytically solvable eigenvalue problem for the linear elasticity equations.
Day, David Minot; Romero, Louis Anthony
2004-07-01
Analytic solutions are useful for code verification. Structural vibration codes approximate solutions to the eigenvalue problem for the linear elasticity equations (Navier's equations). Unfortunately the verification method of 'manufactured solutions' does not apply to vibration problems. Verification books (for example [2]) tabulate a few of the lowest modes, but are not useful for computations of large numbers of modes. A closed form solution is presented here for all the eigenvalues and eigenfunctions for a cuboid solid with isotropic material properties. The boundary conditions correspond physically to a greased wall.
Hlaing, Lwin Mar; Fahmida, Umi; Htet, Min Kyaw; Utomo, Budi; Firmansyah, Agus; Ferguson, Elaine L
2016-07-01
Poor feeding practices result in inadequate nutrient intakes in young children in developing countries. To improve practices, local food-based complementary feeding recommendations (CFR) are needed. This cross-sectional survey aimed to describe current food consumption patterns of 12-23-month-old Myanmar children (n 106) from Ayeyarwady region in order to identify nutrient requirements that are difficult to achieve using local foods and to formulate affordable and realistic CFR to improve dietary adequacy. Weekly food consumption patterns were assessed using a 12-h weighed dietary record, single 24-h recall and a 5-d food record. Food costs were estimated by market surveys. CFR were formulated by linear programming analysis using WHO Optifood software and evaluated among mothers (n 20) using trial of improved practices (TIP). Findings showed that Ca, Zn, niacin, folate and Fe were 'problem nutrients': nutrients that did not achieve 100 % recommended nutrient intake even when the diet was optimised. Chicken liver, anchovy and roselle leaves were locally available nutrient-dense foods that would fill these nutrient gaps. The final set of six CFR would ensure dietary adequacy for five of twelve nutrients at a minimal cost of 271 kyats/d (based on the exchange rate of 900 kyats/USD at the time of data collection: 3rd quarter of 2012), but inadequacies remained for niacin, folate, thiamin, Fe, Zn, Ca and vitamin B6. TIP showed that mothers believed liver and vegetables would cause worms and diarrhoea, but these beliefs could be overcome to successfully promote liver consumption. Therefore, an acceptable set of CFR were developed to improve the dietary practices of 12-23-month-old Myanmar children using locally available foods. Alternative interventions such as fortification, however, are still needed to ensure dietary adequacy of all nutrients. PMID:26696232
Analysing seismic-source mechanisms by linear-programming methods.
Julian, B.R.
1986-01-01
Linear-programming methods are powerful and efficient tools for objectively analysing seismic focal mechanisms and are applicable to a wide range of problems, including tsunami warning and nuclear explosion identification. The source mechanism is represented as a point in the 6-D space of moment-tensor components. The present method can easily be extended to fit observed seismic-wave amplitudes (either signed or absolute) subject to polarity constraints, and to assess the range of mechanisms consistent with a set of measured amplitudes. -from Author
A scalable parallel algorithm for multiple objective linear programs
NASA Technical Reports Server (NTRS)
Wiecek, Malgorzata M.; Zhang, Hong
1994-01-01
This paper presents an ADBASE-based parallel algorithm for solving multiple objective linear programs (MOLP's). Job balance, speedup and scalability are of primary interest in evaluating efficiency of the new algorithm. Implementation results on Intel iPSC/2 and Paragon multiprocessors show that the algorithm significantly speeds up the process of solving MOLP's, which is understood as generating all or some efficient extreme points and unbounded efficient edges. The algorithm gives specially good results for large and very large problems. Motivation and justification for solving such large MOLP's are also included.
The Effect of Data Scaling on Dual Prices and Sensitivity Analysis in Linear Programs
ERIC Educational Resources Information Center
Adlakha, V. G.; Vemuganti, R. R.
2007-01-01
In many practical situations scaling the data is necessary to solve linear programs. This note explores the relationships in translating the sensitivity analysis between the original and the scaled problems.
User's manual for interactive LINEAR: A FORTRAN program to derive linear aircraft models
NASA Technical Reports Server (NTRS)
Antoniewicz, Robert F.; Duke, Eugene L.; Patterson, Brian P.
1988-01-01
An interactive FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft aerodynamic models is documented in this report. The program LINEAR numerically determines a linear system model using nonlinear equations of motion and a user-supplied linear or nonlinear aerodynamic model. The nonlinear equations of motion used are six-degree-of-freedom equations with stationary atmosphere and flat, nonrotating earth assumptions. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model.
An algorithm for the solution of dynamic linear programs
NASA Technical Reports Server (NTRS)
Psiaki, Mark L.
1989-01-01
The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation
Using linear programming to minimize the cost of nurse personnel.
Matthews, Charles H
2005-01-01
Nursing personnel costs make up a major portion of most hospital budgets. This report evaluates and optimizes the utility of the nurse personnel at the Internal Medicine Outpatient Clinic of Wake Forest University Baptist Medical Center. Linear programming (LP) was employed to determine the effective combination of nurses that would allow for all weekly clinic tasks to be covered while providing the lowest possible cost to the department. Linear programming is a standard application of standard spreadsheet software that allows the operator to establish the variables to be optimized and then requires the operator to enter a series of constraints that will each have an impact on the ultimate outcome. The application is therefore able to quantify and stratify the nurses necessary to execute the tasks. With the report, a specific sensitivity analysis can be performed to assess just how sensitive the outcome is to the stress of adding or deleting a nurse to or from the payroll. The nurse employee cost structure in this study consisted of five certified nurse assistants (CNA), three licensed practicing nurses (LPN), and five registered nurses (RN). The LP revealed that the outpatient clinic should staff four RNs, three LPNs, and four CNAs with 95 percent confidence of covering nurse demand on the floor. This combination of nurses would enable the clinic to: 1. Reduce annual staffing costs by 16 percent; 2. Force each level of nurse to be optimally productive by focusing on tasks specific to their expertise; 3. Assign accountability more efficiently as the nurses adhere to their specific duties; and 4. Ultimately provide a competitive advantage to the clinic as it relates to nurse employee and patient satisfaction. Linear programming can be used to solve capacity problems for just about any staffing situation, provided the model is indeed linear. PMID:18972976
Optimization Research of Generation Investment Based on Linear Programming Model
NASA Astrophysics Data System (ADS)
Wu, Juan; Ge, Xueqian
Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.
Rees algebras, Monomial Subrings and Linear Optimization Problems
NASA Astrophysics Data System (ADS)
Dupont, Luis A.
2010-06-01
In this thesis we are interested in studying algebraic properties of monomial algebras, that can be linked to combinatorial structures, such as graphs and clutters, and to optimization problems. A goal here is to establish bridges between commutative algebra, combinatorics and optimization. We study the normality and the Gorenstein property-as well as the canonical module and the a-invariant-of Rees algebras and subrings arising from linear optimization problems. In particular, we study algebraic properties of edge ideals and algebras associated to uniform clutters with the max-flow min-cut property or the packing property. We also study algebraic properties of symbolic Rees algebras of edge ideals of graphs, edge ideals of clique clutters of comparability graphs, and Stanley-Reisner rings.
Efficient algorithms for linear dynamic inverse problems with known motion
NASA Astrophysics Data System (ADS)
Hahn, B. N.
2014-03-01
An inverse problem is called dynamic if the object changes during the data acquisition process. This occurs e.g. in medical applications when fast moving organs like the lungs or the heart are imaged. Most regularization methods are based on the assumption that the object is static during the measuring procedure. Hence, their application in the dynamic case often leads to serious motion artefacts in the reconstruction. Therefore, an algorithm has to take into account the temporal changes of the investigated object. In this paper, a reconstruction method that compensates for the motion of the object is derived for dynamic linear inverse problems. The algorithm is validated at numerical examples from computerized tomography.
NASA Astrophysics Data System (ADS)
Kreischer, K. E.
1982-01-01
A program which calculates the linear characteristics of a gyrotron is presented. This program is capable of: (1) calculating the starting current or frequency detuning for each gyrotron mode; (2) generating mode spectra; (3) plotting these linear characteristics as a function of device parameters; and (4) doing the above for any axial RF field profile.
Split diversity in constrained conservation prioritization using integer linear programming
Chernomor, Olga; Minh, Bui Quang; Forest, Félix; Klaere, Steffen; Ingram, Travis; Henzinger, Monika; von Haeseler, Arndt
2015-01-01
Phylogenetic diversity (PD) is a measure of biodiversity based on the evolutionary history of species. Here, we discuss several optimization problems related to the use of PD, and the more general measure split diversity (SD), in conservation prioritization. Depending on the conservation goal and the information available about species, one can construct optimization routines that incorporate various conservation constraints. We demonstrate how this information can be used to select sets of species for conservation action. Specifically, we discuss the use of species' geographic distributions, the choice of candidates under economic pressure, and the use of predator–prey interactions between the species in a community to define viability constraints. Despite such optimization problems falling into the area of NP hard problems, it is possible to solve them in a reasonable amount of time using integer programming. We apply integer linear programming to a variety of models for conservation prioritization that incorporate the SD measure. We exemplarily show the results for two data sets: the Cape region of South Africa and a Caribbean coral reef community. Finally, we provide user-friendly software at http://www.cibiv.at/software/pda. PMID:25893087
Moryakov, A. V. Pylyov, S. S.
2012-12-15
This paper presents the formulation of the problem and the methodical approach for solving large systems of linear differential equations describing nonstationary processes with the use of CUDA technology; this approach is implemented in the ANGEL program. Results for a test problem on transport of radioactive products over loops of a nuclear power plant are given. The possibilities for the use of the ANGEL program for solving various problems that simulate arbitrary nonstationary processes are discussed.
NASA Technical Reports Server (NTRS)
Bowman, L. M.
1984-01-01
An interactive steady state frequency response computer program with graphics is documented. Single or multiple forces may be applied to the structure using a modal superposition approach to calculate response. The method can be reapplied to linear, proportionally damped structures in which the damping may be viscous or structural. The theoretical approach and program organization are described. Example problems, user instructions, and a sample interactive session are given to demonstate the program's capability in solving a variety of problems.
Accurate construction of consensus genetic maps via integer linear programming.
Wu, Yonghui; Close, Timothy J; Lonardi, Stefano
2011-01-01
We study the problem of merging genetic maps, when the individual genetic maps are given as directed acyclic graphs. The computational problem is to build a consensus map, which is a directed graph that includes and is consistent with all (or, the vast majority of) the markers in the input maps. However, when markers in the individual maps have ordering conflicts, the resulting consensus map will contain cycles. Here, we formulate the problem of resolving cycles in the context of a parsimonious paradigm that takes into account two types of errors that may be present in the input maps, namely, local reshuffles and global displacements. The resulting combinatorial optimization problem is, in turn, expressed as an integer linear program. A fast approximation algorithm is proposed, and an additional speedup heuristic is developed. Our algorithms were implemented in a software tool named MERGEMAP which is freely available for academic use. An extensive set of experiments shows that MERGEMAP consistently outperforms JOINMAP, which is the most popular tool currently available for this task, both in terms of accuracy and running time. MERGEMAP is available for download at http://www.cs.ucr.edu/~yonghui/mgmap.html. PMID:20479505
Program Budgeting: Promise and Problems.
ERIC Educational Resources Information Center
Huff, Robert A.
Planning, Programming, and Budgeting Systems (PPBS) are increasingly mentioned as effective means for improving the management of educational resources in institutions of higher education. PPBS has several advantages over conventional accounting systems, which still would be needed for day to day operations. First, it relates cost to output;…
Some problems in applications of the linear variational method
NASA Astrophysics Data System (ADS)
Pupyshev, Vladimir I.; Montgomery, H. E.
2015-09-01
The linear variational method is a standard computational method in quantum mechanics and quantum chemistry. As taught in most classes, the general guidance is to include as many basis functions as practical in the variational wave function. However, if it is desired to study the patterns of energy change accompanying the change of system parameters such as the shape and strength of the potential energy, the problem becomes more complicated. We use one-dimensional systems with a particle in a rectangular or in a harmonic potential confined in an infinite rectangular box to illustrate situations where a variational calculation can give incorrect results. These situations result when the energy of the lowest eigenvalue is strongly dependent on the parameters that describe the shape and strength of the potential. The numerical examples described in this work are provided as cautionary notes for practitioners of numerical variational calculations.
Using parallel banded linear system solvers in generalized eigenvalue problems
NASA Technical Reports Server (NTRS)
Zhang, Hong; Moss, William F.
1993-01-01
Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speed-up is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.
First integrals for the Kepler problem with linear drag
NASA Astrophysics Data System (ADS)
Margheri, Alessandro; Ortega, Rafael; Rebelo, Carlota
2016-07-01
In this work we consider the Kepler problem with linear drag, and prove the existence of a continuous vector-valued first integral, obtained taking the limit as t→ +∞ of the Runge-Lenz vector. The norm of this first integral can be interpreted as an asymptotic eccentricity e_{∞} with 0≤ e_{∞} ≤ 1 . The orbits satisfying e_{∞} <1 approach the singularity by an elliptic spiral and the corresponding solutions x(t)=r(t)e^{iθ (t)} have a norm r(t) that goes to zero like a negative exponential and an argument θ (t) that goes to infinity like a positive exponential. In particular, the difference between consecutive times of passage through the pericenter, say T_{n+1} -T_n , goes to zero as 1/n.
Polynomial interior-point algorithms for horizontal linear complementarity problem
NASA Astrophysics Data System (ADS)
Wang, G. Q.; Bai, Y. Q.
2009-11-01
In this paper a class of polynomial interior-point algorithms for horizontal linear complementarity problem based on a new parametric kernel function, with parameters p[set membership, variant][0,1] and [sigma]>=1, are presented. The proposed parametric kernel function is not exponentially convex and also not strongly convex like the usual kernel functions, and has a finite value at the boundary of the feasible region. It is used both for determining the search directions and for measuring the distance between the given iterate and the [mu]-center for the algorithm. The currently best known iteration bounds for the algorithm with large- and small-update methods are derived, namely, and , respectively, which reduce the gap between the practical behavior of the algorithms and their theoretical performance results. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p,[sigma] and [theta].
LINPRO: Linear inverse problem library for data contaminated by statistical noise
NASA Astrophysics Data System (ADS)
Magierski, Piotr; Wlazłowski, Gabriel
2012-10-01
The library LINPRO which provides the solution to the linear inverse problem for data contaminated by a statistical noise is presented. The library makes use of two methods: Maximum Entropy Method and Singular Value Decomposition. As an example it has been applied to perform an analytic continuation of the imaginary time propagator obtained within the Quantum Monte Carlo method. Program summary Program title: LINPRO v1.0. Catalogue identifier: AEMT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMT_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland. Licensing provisions: GNU Lesser General Public Licence. No. of lines in distributed program, including test data, etc.: 110620. No. of bytes in distributed program, including test data, etc.: 3208593. Distribution format: tar.gz. Programming language: C++. Computer: LINPRO library should compile on any computing system that has C++ compiler. Operating system: Linux or Unix. Classification: 4.9, 4.12, 4.13. External routines: OPT++: An Object-Oriented Nonlinear Optimization Library [1] (included in the distribution). Nature of problem: LINPRO library solves linear inverse problems with an arbitrary kernel and arbitrary external constraints imposed on the solution. Solution method: LINPRO library implements two complementary methods: Maximum Entropy Method and SVD method. Additional comments: Tested with compilers-GNU Compiler g++, Intel Compiler icpc. Running time: Problem dependent, ranging from seconds to hours. Each of the examples takes less than a minute to run. References: [1] OPT++: An Object-Oriented Nonlinear Optimization Library, https://software.sandia.gov/opt++/.
On-Off Minimum-Time Control With Limited Fuel Usage: Global Optima Via Linear Programming
DRIESSEN,BRIAN
1999-09-01
A method for finding a global optimum to the on-off minimum-time control problem with limited fuel usage is presented. Each control can take on only three possible values: maximum, zero, or minimum. The simplex method for linear systems naturally yields such a solution for the re-formulation presented herein because it always produces an extreme point solution to the linear program. Numerical examples for the benchmark linear flexible system are presented.
Application of fuzzy linear programming to maintenance scheduling
Noor, S.F.; McDonald, J.R.
1995-10-01
In this paper initially, methods of fuzzy linear programming are discussed, which is then followed by an explanation of fuzzy 0-1 programming and finally the authors show how this method is applied to maintenance scheduling of a series of generators. Fuzzy linear 0-1 programming may be used for maintenance scheduling of generating units, this makes it possible to represent some of the maintenance constraints in flexible form and hence better suited to the requirements of maintenance personnel.
Dynamic programming in applied optimization problems
NASA Astrophysics Data System (ADS)
Zavalishchin, Dmitry
2015-11-01
Features of the use dynamic programming in applied problems are investigated. In practice such problems as finding the critical paths in network planning and control, finding the optimal supply plan in transportation problem, objects territorial distribution are traditionally solved by special methods of operations research. It should be noted that the dynamic programming is not provided computational advantages, but facilitates changes and modifications of tasks. This follows from the Bellman's optimality principle. The features of the multistage decision processes construction in applied problems are provided.
Measuring Astronomical Distances with Linear Programming
ERIC Educational Resources Information Center
Narain, Akshar
2015-01-01
A few years ago it was suggested that the distance to celestial bodies could be computed by tracking their position over about 24 hours and then solving a regression problem. One only needed to use inexpensive telescopes, cameras, and astrometry tools, and the experiment could be done from one's backyard. However, it is not obvious to an amateur…
Micosoft Excel Sensitivity Analysis for Linear and Stochastic Program Feed Formulation
Technology Transfer Automated Retrieval System (TEKTRAN)
Sensitivity analysis is a part of mathematical programming solutions and is used in making nutritional and economic decisions for a given feed formulation problem. The terms, shadow price and reduced cost, are familiar linear program (LP) terms to feed formulators. Because of the nonlinear nature of...
Algorithm 937: MINRES-QLP for Symmetric and Hermitian Linear Equations and Least-Squares Problems.
Choi, Sou-Cheng T; Saunders, Michael A
2014-02-01
We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite pre-conditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program units. In particular, we circumvent the need for reverse communication. Example test programs input and solve real or complex problems specified in Matrix Market format. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP. PMID:25328255
Algorithm 937: MINRES-QLP for Symmetric and Hermitian Linear Equations and Least-Squares Problems
Choi, Sou-Cheng T.; Saunders, Michael A.
2014-01-01
We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite pre-conditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program units. In particular, we circumvent the need for reverse communication. Example test programs input and solve real or complex problems specified in Matrix Market format. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP. PMID:25328255
SUBOPT: A CAD program for suboptimal linear regulators
NASA Technical Reports Server (NTRS)
Fleming, P. J.
1985-01-01
An interactive software package which provides design solutions for both standard linear quadratic regulator (LQR) and suboptimal linear regulator problems is described. Intended for time-invariant continuous systems, the package is easily modified to include sampled-data systems. LQR designs are obtained by established techniques while the large class of suboptimal problems containing controller and/or performance index options is solved using a robust gradient minimization technique. Numerical examples demonstrate features of the package and recent developments are described.
The treatment of contact problems as a non-linear complementarity problem
Bjorkman, G.
1994-12-31
Contact and friction problems are of great importance in many engineering applications, for example in ball bearings, bolted joints, metal forming and also car crashes. In these problems the behavior on the contact surface has a great influence on the overall behavior of the structure. Often problems such as wear and initiation of cracks occur on the contact surface. Contact problems are often described using complementarity conditions, w {>=} 0, p {>=} 0, w{sup T}p = 0, which for example represents the following behavior: (i) two bodies can not penetrate each other, i.e. the gap must be greater than or equal to zero, (ii) the contact pressure is positive and different from zero only if the two bodies are in contact with each other. Here it is shown that by using the theory of non-linear complementarity problems the unilateral behavior of the problem can be treated in a straightforward way. It is shown how solution methods for discretized frictionless contact problem can be formulated. By formulating the problem either as a generalized equation or as a B-differentiable function, it is pointed out how Newton`s method may be extended to contact problems. Also an algorithm for tracing the equilibrium path of frictionless contact problems is described. It is shown that, in addition to the {open_quotes}classical{close_quotes} bifurcation and limit points, there can be points where the equilibrium path has reached an end point or points where bifurcation is possible even if the stiffness matrix is non-singular.
Problem Solving. Workplace Education Program Curriculum.
ERIC Educational Resources Information Center
Burkhart, Jennifer
The BUILD Program (Businesses United to Increase Literacy Development) was conducted from June 1991 through December 1992 as a cooperative workplace literacy program joining Arapahoe Community College and four companies in Littleton, Colorado. This document consists of three modules for the problem-solving and computer learning systems classes of…
Application of fractional derivative models in linear viscoelastic problems
NASA Astrophysics Data System (ADS)
Sasso, M.; Palmieri, G.; Amodio, D.
2011-11-01
Appropriate knowledge of viscoelastic properties of polymers and elastomers is of fundamental importance for a correct modelization and analysis of structures where such materials are present, especially when dealing with dynamic and vibration problems. In this paper experimental results of a series of compression and tension tests on specimens of styrene-butadiene rubber and polypropylene plastic are presented; tests consist of creep and relaxation tests, as well as cyclic loading at different frequencies. Experimental data are then used to calibrate some linear viscoelastic models; besides the classical approach based on a combination in series or parallel of standard mechanical elements as springs and dashpots, particular emphasis is given to the application of models whose constitutive equations are based on differential equations of fractional order (Fractional Derivative Model). The two approaches are compared analyzing their capability to reproduce all the experimental data for given materials; also, the main computational issues related with these models are addressed, and the advantage of using a limited number of parameters is demonstrated.
Approximate labeling via graph cuts based on linear programming.
Komodakis, Nikos; Tziritas, Georgios
2007-08-01
A new framework is presented for both understanding and developing graph-cut-based combinatorial algorithms suitable for the approximate optimization of a very wide class of Markov Random Fields (MRFs) that are frequently encountered in computer vision. The proposed framework utilizes tools from the duality theory of linear programming in order to provide an alternative and more general view of state-of-the-art techniques like the \\alpha-expansion algorithm, which is included merely as a special case. Moreover, contrary to \\alpha-expansion, the derived algorithms generate solutions with guaranteed optimality properties for a much wider class of problems, for example, even for MRFs with nonmetric potentials. In addition, they are capable of providing per-instance suboptimality bounds in all occasions, including discrete MRFs with an arbitrary potential function. These bounds prove to be very tight in practice (that is, very close to 1), which means that the resulting solutions are almost optimal. Our algorithms' effectiveness is demonstrated by presenting experimental results on a variety of low-level vision tasks, such as stereo matching, image restoration, image completion, and optical flow estimation, as well as on synthetic problems. PMID:17568146
The RANDOM computer program: A linear congruential random number generator
NASA Technical Reports Server (NTRS)
Miles, R. F., Jr.
1986-01-01
The RANDOM Computer Program is a FORTRAN program for generating random number sequences and testing linear congruential random number generators (LCGs). The linear congruential form of random number generator is discussed, and the selection of parameters of an LCG for a microcomputer described. This document describes the following: (1) The RANDOM Computer Program; (2) RANDOM.MOD, the computer code needed to implement an LCG in a FORTRAN program; and (3) The RANCYCLE and the ARITH Computer Programs that provide computational assistance in the selection of parameters for an LCG. The RANDOM, RANCYCLE, and ARITH Computer Programs are written in Microsoft FORTRAN for the IBM PC microcomputer and its compatibles. With only minor modifications, the RANDOM Computer Program and its LCG can be run on most micromputers or mainframe computers.
Experience with two parallel programs solving the traveling salesman problem
Mohan, J.
1983-01-01
The traveling salesman problem is solved on CM*, a multiprocessor system, using two parallel search programs based on the branch and bound algorithm of Little, Murty, Sweeny and Karel. One of these programs is synchronous and has a master-slave process structure, while the other is asynchronous and has an egalitarian structure. The absolute execution times and the speedups of the two programs differ significantly. Their execution times differ because of the difference in their process structure. Their speedups differ because they require different amounts of computation to solve the same problem. This difference in the amount of computation is explained by their different heuristic granularities. The difference between the speedup of the asynchronous second program and linear speedup is attributed to processors idling owing to resource contention. 6 references.
Dynamic Programming for Structured Continuous Markov Decision Problems
NASA Technical Reports Server (NTRS)
Dearden, Richard; Meuleau, Nicholas; Washington, Richard; Feng, Zhengzhu
2004-01-01
We describe an approach for exploiting structure in Markov Decision Processes with continuous state variables. At each step of the dynamic programming, the state space is dynamically partitioned into regions where the value function is the same throughout the region. We first describe the algorithm for piecewise constant representations. We then extend it to piecewise linear representations, using techniques from POMDPs to represent and reason about linear surfaces efficiently. We show that for complex, structured problems, our approach exploits the natural structure so that optimal solutions can be computed efficiently.
A linear analytical boundary element method (BEM) for 2D homogeneous potential problems
NASA Astrophysics Data System (ADS)
Friedrich, Jürgen
2002-06-01
The solution of potential problems is not only fundamental for geosciences, but also an essential part of related subjects like electro- and fluid-mechanics. In all fields, solution algorithms are needed that should be as accurate as possible, robust, simple to program, easy to use, fast and small in computer memory. An ideal technique to fulfill these criteria is the boundary element method (BEM) which applies Green's identities to transform volume integrals into boundary integrals. This work describes a linear analytical BEM for 2D homogeneous potential problems that is more robust and precise than numerical methods because it avoids numerical schemes and coordinate transformations. After deriving the solution algorithm, the introduced approach is tested against different benchmarks. Finally, the gained method was incorporated into an existing software program described before in this journal by the same author.
The Intelligence of Dual Simplex Method to Solve Linear Fractional Fuzzy Transportation Problem
Narayanamoorthy, S.; Kalyani, S.
2015-01-01
An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example. PMID:25810713
Application of linear programming techniques for controlling linear dynamic plants in real time
NASA Astrophysics Data System (ADS)
Gabasov, R.; Kirillova, F. M.; Ha, Vo Thi Thanh
2016-03-01
The problem of controlling a linear dynamic plant in real time given its nondeterministic model and imperfect measurements of the inputs and outputs is considered. The concepts of current distributions of the initial state and disturbance parameters are introduced. The method for the implementation of disclosable loop using the separation principle is described. The optimal control problem under uncertainty conditions is reduced to the problems of optimal observation, optimal identification, and optimal control of the deterministic system. To extend the domain where a solution to the optimal control problem under uncertainty exists, a two-stage optimal control method is proposed. Results are illustrated using a dynamic plant of the fourth order.
NASA Technical Reports Server (NTRS)
Frost, Susan A.; Bodson, Marc; Acosta, Diana M.
2009-01-01
The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.
Interactive Problem Solving Tutorials Through Visual Programming
NASA Astrophysics Data System (ADS)
Undreiu, Lucian; Schuster, David; Undreiu, Adriana
2008-10-01
We have used LabVIEW visual programming to build an interactive tutorial to promote conceptual understanding in physics problem solving. This programming environment is able to offer a web-accessible problem solving experience that enables students to work at their own pace and receive feedback. Intuitive graphical symbols, modular structures and the ability to create templates are just a few of the advantages this software has to offer. The architecture of an application can be designed in a way that allows instructors with little knowledge of LabVIEW to easily personalize it. Both the physics solution and the interactive pedagogy can be visually programmed in LabVIEW. Our physics pedagogy approach is that of cognitive apprenticeship, in that the tutorial guides students to develop conceptual understanding and physical insight into phenomena, rather than purely formula-based solutions. We demonstrate how this model is reflected in the design and programming of the interactive tutorials.
Fast pricing of American options by linear programming
Dempster, M.; Hutton, J.P.
1994-12-31
This paper describes a new method for computation of the value of various American options on underlying dividend bearing securities under standard Black-Scholes assumptions. It is well known that the problem of valuing the American put can be expressed as solving an abstract linear complementarity problem in terms of a parabolic partial differential operator. Generalizing earlier work of Cryer, Dempster and Borwein for elliptic operators, we show that the American put option value function is the solution of an abstract linear programme bounded by the payoff at exercise. Different American options require only different payoff function bounds. Standard finite difference or finite element approximations to the complementarity problem lead to ordinary linear programmes. We report promising computational results for several American option types using IBM`s Optimization System Library on an RS6000/590.
Program Helps Decompose Complicated Design Problems
NASA Technical Reports Server (NTRS)
Rogers, James L., Jr.
1993-01-01
Time saved by intelligent decomposition into smaller, interrelated problems. DeMAID is knowledge-based software system for ordering sequence of modules and identifying possible multilevel structure for design problem. Displays modules in N x N matrix format. Requires investment of time to generate and refine list of modules for input, it saves considerable amount of money and time in total design process, particularly new design problems in which ordering of modules has not been defined. Program also implemented to examine assembly-line process or ordering of tasks and milestones.
Multigrid approaches to non-linear diffusion problems on unstructured meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.
Employee assistance program treats personal problems.
Bednarek, R J; Featherston, H J
1984-03-01
Though the concept of employee assistance programs (EAPs) is widely accepted throughout business and industry, few hospitals have established similar channels for dealing with workers whose personal problems cause work-related problems. Among the reasons for the health care profession's lack of involvement in this area are: lack of information about costs and benefits of EAPs; the hospital's multidisciplinary environment in which standards of employee competence and behavior are set by persons from many disciplines; hospital working hours; and health care workers' attitudes about their vulnerability to illness. St. Benedict's Hospital, Ogden, UT, however, has confronted the question of how to demonstrate Christian concern for its employees. St. Benedict's EAP, the Helping Hand, which was created in 1979, combines progressive disciplinary action with the opportunity for early intervention in and treatment of employees' personal problems. When a worker with personal problems is referred to the EAP coordinator, he or she is matched with the appropriate community or hospital resource for treatment. Supervisors are trained to identify employee problems and to focus on employee job performance rather than on attempting to diagnose the problem. St. Benedict's records during the program's first three years illustrate the human benefits as well as the cost savings of an EAP. Of 92 hospital employees who took part in the EAP, 72 improved their situations or resolved their problems. The hospital's turnover rates declined from 36 percent to 20 percent, and approximately $40,800 in turnover and replacement costs were saved. PMID:10317423
A linear-programming approach to temporal reasoning
Jonsson, P.; Baeckstroem, C.
1996-12-31
We present a new formalism, Horn Disjunctive Linear Relations (Horn DLRs), for reasoning about temporal constraints. We prove that deciding satisfiability of sets of Horn DLRs is polynomial by exhibiting an algorithm based upon linear programming. Furthermore, we prove that most other approaches to tractable temporal constraint reasoning can be encoded as Horn DLRs, including the ORD-Horn algebra and most methods for purely quantitative reasoning.
A Mixed Integer Linear Program for Airport Departure Scheduling
NASA Technical Reports Server (NTRS)
Gupta, Gautam; Jung, Yoon Chul
2009-01-01
Aircraft departing from an airport are subject to numerous constraints while scheduling departure times. These constraints include wake-separation constraints for successive departures, miles-in-trail separation for aircraft bound for the same departure fixes, and time-window or prioritization constraints for individual flights. Besides these, emissions as well as increased fuel consumption due to inefficient scheduling need to be included. Addressing all the above constraints in a single framework while allowing for resequencing of the aircraft using runway queues is critical to the implementation of the Next Generation Air Transport System (NextGen) concepts. Prior work on airport departure scheduling has addressed some of the above. However, existing methods use pre-determined runway queues, and schedule aircraft from these departure queues. The source of such pre-determined queues is not explicit, and could potentially be a subjective controller input. Determining runway queues and scheduling within the same framework would potentially result in better scheduling. This paper presents a mixed integer linear program (MILP) for the departure-scheduling problem. The program takes as input the incoming sequence of aircraft for departure from a runway, along with their earliest departure times and an optional prioritization scheme based on time-window of departure for each aircraft. The program then assigns these aircraft to the available departure queues and schedules departure times, explicitly considering wake separation and departure fix restrictions to minimize total delay for all aircraft. The approach is generalized and can be used in a variety of situations, and allows for aircraft prioritization based on operational as well as environmental considerations. We present the MILP in the paper, along with benefits over the first-come-first-serve (FCFS) scheme for numerous randomized problems based on real-world settings. The MILP results in substantially reduced
Problems with the linear q-Fokker Planck equation
NASA Astrophysics Data System (ADS)
Yano, Ryosuke
2015-05-01
In this letter, we discuss the linear q-Fokker Planck equation, whose solution follows Tsallis distribution, from the viewpoint of kinetic theory. Using normal definitions of moments, we can expand the distribution function with infinite moments for 0 ⩽ q < 1, whereas we cannot expand the distribution function with infinite moments for 1 < q owing to emergences of characteristic points in moments. From Grad's 13 moment equations for the linear q-Fokker Planck equation, the dissipation rate of the heat flux via the linear q-Fokker Planck equation diverges at 0 ⩽ q < 2/3. In other words, the thermal conductivity, which defines the heat flux with the spatial gradient of the temperature and the thermal conductivity, which defines the heat flux with the spacial gradient of the density, jumps to zero at q = 2/3, discontinuously.
Linear combination reading program for capture gamma rays
Tanner, Allan B.
1971-01-01
This program computes a weighting function, Qj, which gives a scalar output value of unity when applied to the spectrum of a desired element and a minimum value (considering statistics) when applied to spectra of materials not containing the desired element. Intermediate values are obtained for materials containing the desired element, in proportion to the amount of the element they contain. The program is written in the BASIC language in a format specific to the Hewlett-Packard 2000A Time-Sharing System, and is an adaptation of an earlier program for linear combination reading for X-ray fluorescence analysis (Tanner and Brinkerhoff, 1971). Following the program is a sample run from a study of the application of the linear combination technique to capture-gamma-ray analysis for calcium (report in preparation).
Fixed Point Problems for Linear Transformations on Pythagorean Triples
ERIC Educational Resources Information Center
Zhan, M.-Q.; Tong, J.-C.; Braza, P.
2006-01-01
In this article, an attempt is made to find all linear transformations that map a standard Pythagorean triple (a Pythagorean triple [x y z][superscript T] with y being even) into a standard Pythagorean triple, which have [3 4 5][superscript T] as their fixed point. All such transformations form a monoid S* under matrix product. It is found that S*…
A linear regression solution to the spatial autocorrelation problem
NASA Astrophysics Data System (ADS)
Griffith, Daniel A.
The Moran Coefficient spatial autocorrelation index can be decomposed into orthogonal map pattern components. This decomposition relates it directly to standard linear regression, in which corresponding eigenvectors can be used as predictors. This paper reports comparative results between these linear regressions and their auto-Gaussian counterparts for the following georeferenced data sets: Columbus (Ohio) crime, Ottawa-Hull median family income, Toronto population density, southwest Ohio unemployment, Syracuse pediatric lead poisoning, and Glasgow standard mortality rates, and a small remotely sensed image of the High Peak district. This methodology is extended to auto-logistic and auto-Poisson situations, with selected data analyses including percentage of urban population across Puerto Rico, and the frequency of SIDs cases across North Carolina. These data analytic results suggest that this approach to georeferenced data analysis offers considerable promise.
An alternative method on quadratic programming problems
NASA Astrophysics Data System (ADS)
Dasril, Y.; Mohd, I. B.; Mustaffa, I.; Aminuddin, MMM.
2015-05-01
In this paper we proposed an alternative approach to find the optimum solution of quadratic programming problems (QPP) in its original form without additional information such as slack variable, surplus variable or artificial variable as done in other favourite methods. This approached is based on the violated constraints by the unconstrained optimum. The optimal solution of QPP obtained by searching from initial point to another point alongside of feasible region.
NASA Astrophysics Data System (ADS)
Xu, Jiuping; Li, Jun
2002-09-01
In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduction of random variables' expectation. The reference direction approach is used to deal with linear objectives and results in a linear parametric optimization formula with a single linear objective function. This objective function is combined with the quadratic function using the weighted sums. The quadratic problem is transformed into a linear (parametric) complementary problem, the basic formula for the proposed approach. The sufficient and necessary conditions for (properly, weakly) efficient solutions and some construction characteristics of (weakly) efficient solution sets are obtained. An interactive algorithm is proposed based on reference direction and weighted sums. Varying the parameter vector on the right-hand side of the model, the DM can freely search the efficient frontier with the model. An extended portfolio selection model is formed when liquidity is considered as another objective to be optimized besides expectation and risk. The interactive approach is illustrated with a practical example.
An aftercare program for problem patients.
Wasylenki, D A; Plummer, E; Littmann, S
1981-07-01
The high readmission rates of discharged psychiatric patients have forced mental health professionals to play closer attention to aftercare planning. A program was developed at a psychiatric hospital in Ontario in 1977 to deal with "problem patients"--those who were deemed difficult to place in the community by the referral person or department. The program was characterized by shared institutional-community staffing, systematic aftercare assessment and planning, a crisis intervention approach to discharge, the use of a transitional staff member with patients, and the development of close relationships with community agencies. Study data show that the program was effective in limiting the number of readmissions during its first two years to 20 per cent. PMID:6263785
LFSPMC: Linear feature selection program using the probability of misclassification
NASA Technical Reports Server (NTRS)
Guseman, L. F., Jr.; Marion, B. P.
1975-01-01
The computational procedure and associated computer program for a linear feature selection technique are presented. The technique assumes that: a finite number, m, of classes exists; each class is described by an n-dimensional multivariate normal density function of its measurement vectors; the mean vector and covariance matrix for each density function are known (or can be estimated); and the a priori probability for each class is known. The technique produces a single linear combination of the original measurements which minimizes the one-dimensional probability of misclassification defined by the transformed densities.
NASA Technical Reports Server (NTRS)
Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.
1989-01-01
A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.
NASA Astrophysics Data System (ADS)
Bakker, Lennard F.; Ouyang, Tiancheng; Yan, Duokui; Simmons, Skyler; Roberts, Gareth E.
2010-10-01
We apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four-body problem with masses 1, m, m, 1, and also in a symmetric planar four-body problem with equal masses. In both problems, the assumed symmetries reduce the determination of linear stability to the numerical computation of a single real number. For the collinear problem, this verifies the earlier numerical results of Sweatman for linear stability with respect to collinear and symmetric perturbations.
Algorithmic Trading with Developmental and Linear Genetic Programming
NASA Astrophysics Data System (ADS)
Wilson, Garnett; Banzhaf, Wolfgang
A developmental co-evolutionary genetic programming approach (PAM DGP) and a standard linear genetic programming (LGP) stock trading systemare applied to a number of stocks across market sectors. Both GP techniques were found to be robust to market fluctuations and reactive to opportunities associated with stock price rise and fall, with PAMDGP generating notably greater profit in some stock trend scenarios. Both algorithms were very accurate at buying to achieve profit and selling to protect assets, while exhibiting bothmoderate trading activity and the ability to maximize or minimize investment as appropriate. The content of the trading rules produced by both algorithms are also examined in relation to stock price trend scenarios.
Towards Resolving the Crab Sigma-Problem: A Linear Accelerator?
NASA Technical Reports Server (NTRS)
Contopoulos, Ioannis; Kazanas, Demosthenes; White, Nicholas E. (Technical Monitor)
2002-01-01
Using the exact solution of the axisymmetric pulsar magnetosphere derived in a previous publication and the conservation laws of the associated MHD flow, we show that the Lorentz factor of the outflowing plasma increases linearly with distance from the light cylinder. Therefore, the ratio of the Poynting to particle energy flux, generically referred to as sigma, decreases inversely proportional to distance, from a large value (typically approx. greater than 10(exp 4)) near the light cylinder to sigma approx. = 1 at a transition distance R(sub trans). Beyond this distance the inertial effects of the outflowing plasma become important and the magnetic field geometry must deviate from the almost monopolar form it attains between R(sub lc), and R(sub trans). We anticipate that this is achieved by collimation of the poloidal field lines toward the rotation axis, ensuring that the magnetic field pressure in the equatorial region will fall-off faster than 1/R(sup 2) (R being the cylindrical radius). This leads both to a value sigma = a(sub s) much less than 1 at the nebular reverse shock at distance R(sub s) (R(sub s) much greater than R(sub trans)) and to a component of the flow perpendicular to the equatorial component, as required by observation. The presence of the strong shock at R = R(sub s) allows for the efficient conversion of kinetic energy into radiation. We speculate that the Crab pulsar is unique in requiring sigma(sub s) approx. = 3 x 10(exp -3) because of its small translational velocity, which allowed for the shock distance R(sub s) to grow to values much greater than R(sub trans).
Molecular solutions to the binary integer programming problem based on DNA computation.
Yeh, Chung-Wei; Chu, Chih-Ping; Wu, Kee-Rong
2006-01-01
Binary optimization is a widely investigated topic in integer linear programming. This study proposes a DNA-based computing algorithm for solving the significantly large binary integer programming (BIP) problem. The proposed approach is based upon Adleman and Lipton's DNA operations to solve the BIP problem. The potential of DNA computation for the BIP problem is promising given the operational time complexity of O(nxk). PMID:16229936
NASA Technical Reports Server (NTRS)
Snow, L. S.; Kuhn, A. E.
1975-01-01
Previous error analyses conducted by the Guidance and Dynamics Branch of NASA have used the Guidance Analysis Program (GAP) as the trajectory simulation tool. Plans are made to conduct all future error analyses using the Space Vehicle Dynamics Simulation (SVDS) program. A study was conducted to compare the inertial measurement unit (IMU) error simulations of the two programs. Results of the GAP/SVDS comparison are presented and problem areas encountered while attempting to simulate IMU errors, vehicle performance uncertainties and environmental uncertainties using SVDS are defined. An evaluation of the SVDS linear error analysis capability is also included.
Gene Golub; Kwok Ko
2009-03-30
The solutions of sparse eigenvalue problems and linear systems constitute one of the key computational kernels in the discretization of partial differential equations for the modeling of linear accelerators. The computational challenges faced by existing techniques for solving those sparse eigenvalue problems and linear systems call for continuing research to improve on the algorithms so that ever increasing problem size as required by the physics application can be tackled. Under the support of this award, the filter algorithm for solving large sparse eigenvalue problems was developed at Stanford to address the computational difficulties in the previous methods with the goal to enable accelerator simulations on then the world largest unclassified supercomputer at NERSC for this class of problems. Specifically, a new method, the Hemitian skew-Hemitian splitting method, was proposed and researched as an improved method for solving linear systems with non-Hermitian positive definite and semidefinite matrices.
Global symmetry relations in linear and viscoplastic mobility problems
NASA Astrophysics Data System (ADS)
Kamrin, Ken; Goddard, Joe
2014-11-01
The mobility tensor of a textured surface is a homogenized effective boundary condition that describes the effective slip of a fluid adjacent to the surface in terms of an applied shear traction far above the surface. In the Newtonian fluid case, perturbation analysis yields a mobility tensor formula, which suggests that regardless of the surface texture (i.e. nonuniform hydrophobicity distribution and/or height fluctuations) the mobility tensor is always symmetric. This conjecture is verified using a Lorentz reciprocity argument. It motivates the question of whether such symmetries would arise for nonlinear constitutive relations and boundary conditions, where the mobility tensor is not a constant but a function of the applied stress. We show that in the case of a strongly dissipative nonlinear constitutive relation--one whose strain-rate relates to the stress solely through a scalar Edelen potential--and strongly dissipative surface boundary conditions--one whose hydrophobic character is described by a potential relating slip to traction--the mobility function of the surface also maintains tensorial symmetry. By extension, the same variational arguments can be applied in problems such as the permeability tensor for viscoplastic flow through porous media, and we find that similar symmetries arise. These findings could be used to simplify the characterization of viscoplastic drag in various anisotropic media. (Joe Goddard is a former graduate student of Acrivos).
Solution algorithms for non-linear singularly perturbed optimal control problems
NASA Technical Reports Server (NTRS)
Ardema, M. D.
1983-01-01
The applicability and usefulness of several classical and other methods for solving the two-point boundary-value problem which arises in non-linear singularly perturbed optimal control are assessed. Specific algorithms of the Picard, Newton and averaging types are formally developed for this class of problem. The computational requirements associated with each algorithm are analysed and compared with the computational requirement of the method of matched asymptotic expansions. Approximate solutions to a linear and a non-linear problem are obtained by each method and compared.
Carey, G.F.; Young, D.M.
1993-12-31
The program outlined here is directed to research on methods, algorithms, and software for distributed parallel supercomputers. Of particular interest are finite element methods and finite difference methods together with sparse iterative solution schemes for scientific and engineering computations of very large-scale systems. Both linear and nonlinear problems will be investigated. In the nonlinear case, applications with bifurcation to multiple solutions will be considered using continuation strategies. The parallelizable numerical methods of particular interest are a family of partitioning schemes embracing domain decomposition, element-by-element strategies, and multi-level techniques. The methods will be further developed incorporating parallel iterative solution algorithms with associated preconditioners in parallel computer software. The schemes will be implemented on distributed memory parallel architectures such as the CRAY MPP, Intel Paragon, the NCUBE3, and the Connection Machine. We will also consider other new architectures such as the Kendall-Square (KSQ) and proposed machines such as the TERA. The applications will focus on large-scale three-dimensional nonlinear flow and reservoir problems with strong convective transport contributions. These are legitimate grand challenge class computational fluid dynamics (CFD) problems of significant practical interest to DOE. The methods developed and algorithms will, however, be of wider interest.
Semidefinite programming formulation of linear-scaling electronic structure theories
NASA Astrophysics Data System (ADS)
Veeraraghavan, Srikant; Mazziotti, David A.
2015-08-01
We present a linear-scaling approach based on semidefinite programs (SDPs) to compute the density matrix for effective one-electron theories. Traditional methods constrain the density matrix to represent a Slater determinant and hence rely on parameterization or purification. We eliminate the need for such a constraint by performing an energy minimization over all the convex combinations of density matrices representing Slater determinants. By not relying on purification, the SDP approach not only eliminates accumulation error present in some methods but also reduces the amount of truncation error. Sparsity in the Hamiltonian can be exploited to make the SDP approach scale linearly with system size. Crossovers in computational time with a cubically scaling algorithm are demonstrated for one-dimensional hydrogen chains ranging from H50 to H1500.
LTSTAR- SUPERSONIC WING NON-LINEAR AERODYNAMICS PROGRAM
NASA Technical Reports Server (NTRS)
Carlson, H. W.
1994-01-01
The Supersonic Wing Nonlinear Aerodynamics computer program, LTSTAR, was developed to provide for the estimation of the nonlinear aerodynamic characteristics of a wing at supersonic speeds. This corrected linearized-theory method accounts for nonlinearities in the variation of basic pressure loadings with local surface slopes, predicts the degree of attainment of theoretical leading-edge thrust forces, and provides an estimate of detached leading-edge vortex loadings that result when the theoretical thrust forces are not fully realized. Comparisons of LTSTAR computations with experimental results show significant improvements in detailed wing pressure distributions, particularly for large angles of attack and for regions of the wing where the flow is highly three-dimensional. The program provides generally improved predictions of the wing overall force and moment coefficients. LTSTAR could be useful in design studies aimed at aerodynamic performance optimization and for providing more realistic trade-off information for selection of wing planform geometry and airfoil section parameters. Input to the LTSTAR program includes wing planform data, freestream conditions, wing camber, wing thickness, scaling options, and output options. Output includes pressure coefficients along each chord, section normal and axial force coefficients, and the spanwise distribution of section force coefficients. With the chordwise distributions and section coefficients at each angle of attack, three sets of polars are output. The first set is for linearized theory with and without full leading-edge thrust, the second set includes nonlinear corrections, and the third includes estimates of attainable leading-edge thrust and vortex increments along with the nonlinear corrections. The LTSTAR program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 series computer with a central memory requirement of approximately 150K (octal) of 60 bit words. The LTSTAR
NASA Technical Reports Server (NTRS)
Armstrong, E. S.
1975-01-01
A digital computer program (ORACLS) for implementing the optimal regulator theory approach to the design of controllers for linear time-invariant systems is described. The user-oriented program employs the latest numerical techniques and is applicable to both the digital and continuous control problems.
NASA Technical Reports Server (NTRS)
Nguyen, D. T.; Al-Nasra, M.; Zhang, Y.; Baddourah, M. A.; Agarwal, T. K.; Storaasli, O. O.; Carmona, E. A.
1991-01-01
Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14-16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for nonlinear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on nonlinear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.
Bramble, J.H.; Pasciak, J.E.
1981-01-01
The linearized scalar potential formulation of the magnetostatic field problem is considered. The approach involves a reformulation of the continuous problem as a parametric boundary problem. By the introduction of a spherical interface and the use of spherical harmonics, the infinite boundary condition can also be satisfied in the parametric framework. The reformulated problem is discretized by finite element techniques and a discrete parametric problem is solved by conjugate gradient iteration. This approach decouples the problem in that only standard Neumann type elliptic finite element systems on separate bounded domains need be solved. The boundary conditions at infinity and the interface conditions are satisfied during the boundary parametric iteration.
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Rosen, I. G.
1986-01-01
An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.
NASA Astrophysics Data System (ADS)
Diwaker; Chakraborty, Aniruddha
2015-12-01
In the present work we have reported a simple exact analytical solution to the curve crossing problem of two linear diabatic potentials by transfer matrix method. Our problem assumes the crossing of two linear diabatic potentials which are coupled to each other by an arbitrary coupling (in contrast to linear potentials in the vicinity of crossing points) and for numerical calculation purposes this arbitrary coupling is taken as Gaussian coupling which is further expressed as a collection of Dirac delta functions. Further we calculated the transition probability from one diabatic potential to another by the use of this method.
Illusion of Linearity in Geometry: Effect in Multiple-Choice Problems
ERIC Educational Resources Information Center
Vlahovic-Stetic, Vesna; Pavlin-Bernardic, Nina; Rajter, Miroslav
2010-01-01
The aim of this study was to examine if there is a difference in the performance on non-linear problems regarding age, gender, and solving situation, and whether the multiple-choice answer format influences students' thinking. A total of 112 students, aged 15-16 and 18-19, were asked to solve problems for which solutions based on proportionality…
Fast and Robust Newton strategies for non-linear geodynamics problems
NASA Astrophysics Data System (ADS)
Le Pourhiet, Laetitia; May, Dave
2014-05-01
Geodynamic problems are inherently non-linear, with sources of non-inearities arising from the (i) rheology, (ii) boundary conditions and (iii) the choice of time integration scheme. We have developed a robust non-linear scheme utilizing PETSc's non-linear solver framework; SNES. Through the SNES framework, we have access to a wide range of globalization techniques. In this work we extensively use line search implementation. We explored a wide range different strategies for solving a variety of non-linear problems specific to geodynamics. In this presentation, we report of the most robust line-searching techniques which we have found for the three classes of non-linearities previously identified. Among the class of rheological non-linearities, the shear banding instability using visco-plastic flow rules is the most difficult to solve. Distinctively from its sibling, the elasto-plastic rheology, the visco-plastic rheology causes instantaneous shear localisation. As a results, decreasing time-stepping is not a viable approach to better capture the initial phase of localisation. Furthermore, return map algorithms based on a consistent tangent cannot be used as the slope of the tangent is infinite. Obtaining a converged non-linear solution to this problem only relies on the robustness non-linear solver. After presenting a Newton methodology suitable for rheological non-linearities, we examine the performance of this formulation when frictional sliding boundary conditions are introduced. We assess the robustness of the non-linear solver when applied to critical taper type problems.
NASA Astrophysics Data System (ADS)
Schröder, Jörg; Keip, Marc-André
2012-08-01
The contribution addresses a direct micro-macro transition procedure for electromechanically coupled boundary value problems. The two-scale homogenization approach is implemented into a so-called FE2-method which allows for the computation of macroscopic boundary value problems in consideration of microscopic representative volume elements. The resulting formulation is applicable to the computation of linear as well as nonlinear problems. In the present paper, linear piezoelectric as well as nonlinear electrostrictive material behavior are investigated, where the constitutive equations on the microscale are derived from suitable thermodynamic potentials. The proposed direct homogenization procedure can also be applied for the computation of effective elastic, piezoelectric, dielectric, and electrostrictive material properties.
ERIC Educational Resources Information Center
Moody, John Charles
Assessed were the effects of linear and modified linear programed materials on the achievement of slow learners in tenth grade Biological Sciences Curriculum Study (BSCS) Special Materials biology. Two hundred and six students were randomly placed into four programed materials formats: linear programed materials, modified linear program with…
On high-continuity transfinite element formulations for linear-nonlinear transient thermal problems
NASA Technical Reports Server (NTRS)
Tamma, Kumar K.; Railkar, Sudhir B.
1987-01-01
This paper describes recent developments in the applicability of a hybrid transfinite element methodology with emphasis on high-continuity formulations for linear/nonlinear transient thermal problems. The proposed concepts furnish accurate temperature distributions and temperature gradients making use of a relatively smaller number of degrees of freedom; and the methodology is applicable to linear/nonlinear thermal problems. Characteristic features of the formulations are described in technical detail as the proposed hybrid approach combines the major advantages and modeling features of high-continuity thermal finite elements in conjunction with transform methods and classical Galerkin schemes. Several numerical test problems are evaluated and the results obtained validate the proposed concepts for linear/nonlinear thermal problems.
Some comparison of restarted GMRES and QMR for linear and nonlinear problems
Morgan, R.; Joubert, W.
1994-12-31
Comparisons are made between the following methods: QMR including its transpose-free version, restarted GMRES, and a modified restarted GMRES that uses approximate eigenvectors to improve convergence, For some problems, the modified GMRES is competitive with or better than QMR in terms of the number of matrix-vector products. Also, the GMRES methods can be much better when several similar systems of linear equations must be solved, as in the case of nonlinear problems and ODE problems.
NASA Astrophysics Data System (ADS)
Abramov, A. A.; Yukhno, L. F.
2016-07-01
A nonlinear eigenvalue problem for a linear system of ordinary differential equations is examined on a semi-infinite interval. The problem is supplemented by nonlocal conditions specified by a Stieltjes integral. At infinity, the solution must be bounded. In addition to these basic conditions, the solution must satisfy certain redundant conditions, which are also nonlocal. A numerically stable method for solving such a singular overdetermined eigenvalue problem is proposed and analyzed. The essence of the method is that this overdetermined problem is replaced by an auxiliary problem consistent with all the above conditions.
Initial-value problem for a linear ordinary differential equation of noninteger order
Pskhu, Arsen V
2011-04-30
An initial-value problem for a linear ordinary differential equation of noninteger order with Riemann-Liouville derivatives is stated and solved. The initial conditions of the problem ensure that (by contrast with the Cauchy problem) it is uniquely solvable for an arbitrary set of parameters specifying the orders of the derivatives involved in the equation; these conditions are necessary for the equation under consideration. The problem is reduced to an integral equation; an explicit representation of the solution in terms of the Wright function is constructed. As a consequence of these results, necessary and sufficient conditions for the solvability of the Cauchy problem are obtained. Bibliography: 7 titles.
Research program with no ''measurement problem''
Noyes, H.P.; Gefwert, C.; Manthey, M.J.
1985-07-01
The ''measurement problem'' of contemporary physics is met by recognizing that the physicist participates when constructing and when applying the theory consisting of the formulated formal and measurement criteria (the expressions and rules) providing the necessary conditions which allow him to compute and measure facts, yet retains objectivity by requiring that these criteria, rules and facts be in corroborative equilibrium. We construct the particulate states of quantum physics by a recursive program which incorporates the non-determinism born of communication between asynchronous processes over a shared memory. Their quantum numbers and coupling constants arise from the construction via the unique 4-level combinatorial hierarchy. The construction defines indivisible quantum events with the requisite supraluminal correlations, yet does not allow supraluminal communication. Measurement criteria incorporate c, h-bar, and m/sub p/ or (not ''and'') G. The resulting theory is discrete throughout, contains no infinities, and, as far as we have developed it, is in agreement with quantum mechanical and cosmological fact.
Correlates of Problem-Solving in Programming.
ERIC Educational Resources Information Center
Chung, Choi-man
1988-01-01
Examines some correlates of programing ability that can predict the computer programing performance of students. Finds that students who score high on mathematics and spatial tests will score high on programing ability tests. Finds that boys perform significantly better than girls in programing ability, as do those who possess home computers. (KO)
Microgrid Reliability Modeling and Battery Scheduling Using Stochastic Linear Programming
Cardoso, Goncalo; Stadler, Michael; Siddiqui, Afzal; Marnay, Chris; DeForest, Nicholas; Barbosa-Povoa, Ana; Ferrao, Paulo
2013-05-23
This paper describes the introduction of stochastic linear programming into Operations DER-CAM, a tool used to obtain optimal operating schedules for a given microgrid under local economic and environmental conditions. This application follows previous work on optimal scheduling of a lithium-iron-phosphate battery given the output uncertainty of a 1 MW molten carbonate fuel cell. Both are in the Santa Rita Jail microgrid, located in Dublin, California. This fuel cell has proven unreliable, partially justifying the consideration of storage options. Several stochastic DER-CAM runs are executed to compare different scenarios to values obtained by a deterministic approach. Results indicate that using a stochastic approach provides a conservative yet more lucrative battery schedule. Lower expected energy bills result, given fuel cell outages, in potential savings exceeding 6percent.
Study Abroad Programs: Probleme und Loesungsvorschlage (Problems and Suggested Solutions)
ERIC Educational Resources Information Center
Schild, Kurt W.
1977-01-01
Describes an apparently very successful study program for Americans, conducted by Michigan State University in Mayen, Rheinland-Pfalz. The small (pop. 22,000) non-university city offered many advantages, including relatively low living costs. All students lived with German families. Various contacts are described, including weekend trips. (Text is…
Solution of Mixed-Integer Programming Problems on the XT5
Hartman-Baker, Rebecca J; Busch, Ingrid Karin; Hilliard, Michael R; Middleton, Richard S; Schultze, Michael
2009-01-01
In this paper, we describe our experience with solving difficult mixed-integer linear programming problems (MILPs) on the petaflop Cray XT5 system at the National Center for Computational Sciences at Oak Ridge National Laboratory. We describe the algorithmic, software, and hardware needs for solving MILPs and present the results of using PICO, an open-source, parallel, mixed-integer linear programming solver developed at Sandia National Laboratories, to solve canonical MILPs as well as problems of interest arising from the logistics and supply chain management field.
Djukanovic, M.; Babic, B.; Milosevic, B.; Sobajic, D.J.; Pao, Y.H. |
1996-05-01
In this paper the blending/transloading facilities are modeled using an interactive fuzzy linear programming (FLP), in order to allow the decision-maker to solve the problem of uncertainty of input information within the fuel scheduling optimization. An interactive decision-making process is formulated in which decision-maker can learn to recognize good solutions by considering all possibilities of fuzziness. The application of the fuzzy formulation is accompanied by a careful examination of the definition of fuzziness, appropriateness of the membership function and interpretation of results. The proposed concept provides a decision support system with integration-oriented features, whereby the decision-maker can learn to recognize the relative importance of factors in the specific domain of optimal fuel scheduling (OFS) problem. The formulation of a fuzzy linear programming problem to obtain a reasonable nonfuzzy solution under consideration of the ambiguity of parameters, represented by fuzzy numbers, is introduced. An additional advantage of the FLP formulation is its ability to deal with multi-objective problems.
Conflict Management: A Premarital Training Program in Mutual Problem Solving.
ERIC Educational Resources Information Center
Ridley, Carl A.; And Others
1981-01-01
Evaluated the effectiveness of a structured educational program to train premarital couples in communication and mutual problem-solving skills. Couples (N=26) participated in a problem-solving training program, while similar couples (N=28) participated in a relationship discussion group. The problem-solving group showed a greater increase in…
SLFP: A stochastic linear fractional programming approach for sustainable waste management
Zhu, H.; Huang, G.H.
2011-12-15
Highlights: > A new fractional programming (SLFP) method is developed for waste management. > SLFP can solve ratio optimization problems associated with random inputs. > A case study of waste flow allocation demonstrates its applicability. > SLFP helps compare objectives of two aspects and reflect system efficiency. > This study supports in-depth analysis of tradeoffs among multiple system criteria. - Abstract: A stochastic linear fractional programming (SLFP) approach is developed for supporting sustainable municipal solid waste management under uncertainty. The SLFP method can solve ratio optimization problems associated with random information, where chance-constrained programming is integrated into a linear fractional programming framework. It has advantages in: (1) comparing objectives of two aspects, (2) reflecting system efficiency, (3) dealing with uncertainty expressed as probability distributions, and (4) providing optimal-ratio solutions under different system-reliability conditions. The method is applied to a case study of waste flow allocation within a municipal solid waste (MSW) management system. The obtained solutions are useful for identifying sustainable MSW management schemes with maximized system efficiency under various constraint-violation risks. The results indicate that SLFP can support in-depth analysis of the interrelationships among system efficiency, system cost and system-failure risk.
An iterative method to solve the heat transfer problem under the non-linear boundary conditions
NASA Astrophysics Data System (ADS)
Zhu, Zhenggang; Kaliske, Michael
2012-02-01
The aim of the paper is to determine the approximation of the tangential matrix for solving the non-linear heat transfer problem. Numerical model of the strongly non-linear heat transfer problem based on the theory of the finite element method is presented. The tangential matrix of the Newton method is formulated. A method to solve the heat transfer with the non-linear boundary conditions, based on the secant slope of a reference function, is developed. The contraction mapping principle is introduced to verify the convergence of this method. The application of the method is shown by two examples. Numerical results of these examples are comparable to the ones solved with the Newton method and the commercial software COMSOL for the heat transfer problem under the radiative boundary conditions.
Solving Fractional Programming Problems based on Swarm Intelligence
NASA Astrophysics Data System (ADS)
Raouf, Osama Abdel; Hezam, Ibrahim M.
2014-04-01
This paper presents a new approach to solve Fractional Programming Problems (FPPs) based on two different Swarm Intelligence (SI) algorithms. The two algorithms are: Particle Swarm Optimization, and Firefly Algorithm. The two algorithms are tested using several FPP benchmark examples and two selected industrial applications. The test aims to prove the capability of the SI algorithms to solve any type of FPPs. The solution results employing the SI algorithms are compared with a number of exact and metaheuristic solution methods used for handling FPPs. Swarm Intelligence can be denoted as an effective technique for solving linear or nonlinear, non-differentiable fractional objective functions. Problems with an optimal solution at a finite point and an unbounded constraint set, can be solved using the proposed approach. Numerical examples are given to show the feasibility, effectiveness, and robustness of the proposed algorithm. The results obtained using the two SI algorithms revealed the superiority of the proposed technique among others in computational time. A better accuracy was remarkably observed in the solution results of the industrial application problems.
The Physics Program at the International Linear Collider
NASA Astrophysics Data System (ADS)
Strube, Jan; International Linear Collider Physics; Detector study groups Team
2016-03-01
The precise exploration of all aspects of the Higgs sector is one of the key goals for future colliders at the Energy Frontier. The International Linear Collider (ILC) provides the capability for model-independent measurements of all relevant couplings of the Higgs boson to fermions and gauge bosons, including direct measurements of the Top Yukawa coupling as well as of the Higgs self-coupling. In addition, it has a discovery potential for physics beyond the Standard Model that is complementary to the LHC. This contribution will review the highlights of ILC physics in the context of a 20-year-long program. This program covers different collision energies up to 500 GeV with various beam polarizations, each contributing important aspects to the exploration of this new sector of particle physics. Beyond this initial scope of the ILC, we will also discuss the prospects of a 1 TeV upgrade, which offers complementary capabilities for the measurement of double Higgs production and the Higgs self-coupling and increases the reach of direct and indirect searches. This work is presented on behalf of the groups contributing to ILC physics and detector studies in Asia, Europe and the US.
Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem
Yoo, Jaechil
1996-12-31
Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we prove the convergence of a multigrid (W-cycle) method. This multigrid is robust in that the convergence is uniform as the parameter, v, goes to 1/2 Computational experiments are included.
Wang, C.Y.
1985-01-01
A three-dimensional computer program for linear/non-linear, static/dynamic analyses of reactor-piping systems under various accident loads is described. In the analysis, the hydrodynamic calculation can be performed in the implicit or semi-implicit manner. The structure response can be calculated using either a purely explicit or implicit time-integration scheme. Coupling between the fluid and structure is achieved by utilizing either the implicit-explicit or implicit-implicit link. Thus, a wide range of piping safety problems can be analyzed by the suitable choice of options available in the hydrodynamics and structural analysis. In this paper, several salient features are presented. Sample problems illustrating the versatility of the program are given. The results are discussed in detail.
Weighted linear least squares problem: an interval analysis approach to rank determination
Manteuffel, T. A.
1980-08-01
This is an extension of the work in SAND--80-0655 to the weighted linear least squares problem. Given the weighted linear least squares problem WAx approx. = Wb, where W is a diagonal weighting matrix, and bounds on the uncertainty in the elements of A, we define an interval matrix A/sup I/ that contains all perturbations of A due to these uncertainties and say that the problem is rank deficient if any member of A/sup I/ is rank deficient. It is shown that, if WA = QR is the QR decomposition of WA, then Q and R/sup -1/ can be used to bound the rank of A/sup I/. A modification of the Modified Gram--Schmidt QR decomposition yields an algorithm that implements these results. The extra arithmetic is 0(MN). Numerical results show the algorithm to be effective on problems in which the weights vary greatly in magnitude.
An Application of Parametric Mixed-Integer Linear Programming to Hydropower Development
NASA Astrophysics Data System (ADS)
Turgeon, André
1987-03-01
The problem consists in selecting the sites on the river where reservoirs and hydroelectric power plants are to be built and then determining the type and size of the projected installations. The solution obviously depends on the amount of money the utility is willing to invest, which itself is a function of what the new installations will produce. It is therefore necessary to solve the problem for all possible amounts of firm energy produced, since it is not known at the outset which production level the utility will select. This is done in the paper by a parametric mixed-integer linear programming (MILP) method whose efficiency derives from the fact that the branch-and-bound algorithm for selecting the sites to be developed (and consuming most of the computer time) is solved a minimum number of times. Between the points where the MILP problem is solved, LP parametric analysis is applied.
Preschool-Based Programs for Externalizing Problems
ERIC Educational Resources Information Center
Arnold, David H.; Brown, Sharice A.; Meagher, Susan; Baker, Courtney N.; Dobbs, Jennifer; Doctoroff, Greta L.
2006-01-01
Few mental health initiatives for young children have used classroom programs. Preschool-based efforts targeting externalizing behavior could help prevent conduct disorders. Additional benefits may include improved academic achievement and reduced risk for other mental health difficulties. Pro-grams that target multiple developmental domains are…
Bilingual Program Management: A Problem Solving Approach.
ERIC Educational Resources Information Center
De George, George P., Ed.
A collection of essays on the management of bilingual education programs is organized in three units: managing in a culturally diverse setting, balancing critical interactions, and special issues. The following papers are included: "Recruiting and Retaining Competent Personnel for Bilingual Education Programs" (Joan E. Friedenberg, Curtis H.…
Evaluating the impact of AND/OR search on 0-1 integer linear programming
Dechter, R.
2010-01-01
AND/OR search spaces accommodate advanced algorithmic schemes for graphical models which can exploit the structure of the model. We extend and evaluate the depth-first and best-first AND/OR search algorithms to solving 0-1 Integer Linear Programs (0-1 ILP) within this framework. We also include a class of dynamic variable ordering heuristics while exploring an AND/OR search tree for 0-1 ILPs. We demonstrate the effectiveness of these search algorithms on a variety of benchmarks, including real-world combinatorial auctions, random uncapacitated warehouse location problems and MAX-SAT instances. PMID:21052484
The Use of the Fourier Transform for Solving Linear Elasticity Problems
NASA Astrophysics Data System (ADS)
Kozubek, Tomas; Mocek, Lukas
2011-11-01
This paper deals with solving linear elasticity problems using a modified fictitious domain method and an effective solver based on the discrete Fourier transform and the Schur complement reduction in combination with the null space method. The main goal is to show step by step all ingredients of the numerical solution.
NASA Astrophysics Data System (ADS)
Mocek, Lukas; Kozubek, Tomas
2011-09-01
The paper deals with the numerical solution of elliptic boundary value problems for 2D linear elasticity using the fictitious domain method in combination with the discrete Fourier transform and the FETI domain decomposition. We briefly mention the theoretical background of these methods, introduce resulting solvers, and demonstrate their efficiency on model benchmarks.
High Order Finite Difference Methods, Multidimensional Linear Problems and Curvilinear Coordinates
NASA Technical Reports Server (NTRS)
Nordstrom, Jan; Carpenter, Mark H.
1999-01-01
Boundary and interface conditions are derived for high order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.
Linear Integro-differential Schroedinger and Plate Problems Without Initial Conditions
Lorenzi, Alfredo
2013-06-15
Via Carleman's estimates we prove uniqueness and continuous dependence results for the temporal traces of solutions to overdetermined linear ill-posed problems related to Schroedinger and plate equation. The overdetermination is prescribed in an open subset of the (space-time) lateral boundary.
The problem of scheduling for the linear section of a single-track railway
NASA Astrophysics Data System (ADS)
Akimova, Elena N.; Gainanov, Damir N.; Golubev, Oleg A.; Kolmogortsev, Ilya D.; Konygin, Anton V.
2016-06-01
The paper is devoted to the problem of scheduling for the linear section of a single-track railway: how to organize the flow in both directions in the most efficient way. In this paper, the authors propose an algorithm for scheduling, examine the properties of this algorithm and perform the computational experiments.
Monthly pan evaporation modeling using linear genetic programming
NASA Astrophysics Data System (ADS)
Guven, Aytac; Kisi, Ozgur
2013-10-01
This study compares the accuracy of linear genetic programming (LGP), fuzzy genetic (FG), adaptive neuro-fuzzy inference system (ANFIS), artificial neural networks (ANN) and Stephens-Stewart (SS) methods in modeling pan evaporations. Monthly climatic data including solar radiation, air temperature, relative humidity, wind speed and pan evaporation from Antalya and Mersin stations, in Turkey are used in the study. The study composed of two parts. First part of the study focuses the comparison of LGP models with those of the FG, ANFIS, ANN and SS models in estimating pan evaporations of Antalya and Mersin stations, separately. From the comparison results, the LGP models are found to be better than the other models. Comparison of LGP models with the other models in estimating pan evaporations of the Mersin Station by using both stations' inputs is focused in the second part of the study. The results indicate that the LGP models better accuracy than the FG, ANFIS, ANN and SS models. It is seen that the pan evaporations can be successfully estimated by the LGP method.
Geometric tools for solving the FDI problem for linear periodic discrete-time systems
NASA Astrophysics Data System (ADS)
Longhi, Sauro; Monteriù, Andrea
2013-07-01
This paper studies the problem of detecting and isolating faults in linear periodic discrete-time systems. The aim is to design an observer-based residual generator where each residual is sensitive to one fault, whilst remaining insensitive to the other faults that can affect the system. Making use of the geometric tools, and in particular of the outer observable subspace notion, the Fault Detection and Isolation (FDI) problem is formulated and necessary and solvability conditions are given. An algorithmic procedure is described to determine the solution of the FDI problem.
NASA Technical Reports Server (NTRS)
Kent, James; Holdaway, Daniel
2015-01-01
A number of geophysical applications require the use of the linearized version of the full model. One such example is in numerical weather prediction, where the tangent linear and adjoint versions of the atmospheric model are required for the 4DVAR inverse problem. The part of the model that represents the resolved scale processes of the atmosphere is known as the dynamical core. Advection, or transport, is performed by the dynamical core. It is a central process in many geophysical applications and is a process that often has a quasi-linear underlying behavior. However, over the decades since the advent of numerical modelling, significant effort has gone into developing many flavors of high-order, shape preserving, nonoscillatory, positive definite advection schemes. These schemes are excellent in terms of transporting the quantities of interest in the dynamical core, but they introduce nonlinearity through the use of nonlinear limiters. The linearity of the transport schemes used in Goddard Earth Observing System version 5 (GEOS-5), as well as a number of other schemes, is analyzed using a simple 1D setup. The linearized version of GEOS-5 is then tested using a linear third order scheme in the tangent linear version.
The linearized characteristics method and its application to practical nonlinear supersonic problems
NASA Technical Reports Server (NTRS)
Ferri, Antonio
1952-01-01
The methods of characteristics has been linearized by assuming that the flow field can be represented as a basic flow field determined by nonlinearized methods and a linearized superposed flow field that accounts for small changes of boundary conditions. The method has been applied to two-dimensional rotational flow where the basic flow is potential flow and to axially symmetric problems where conical flows have been used as the basic flows. In both cases the method allows the determination of the flow field to be simplified and the numerical work to be reduced to a few calculations. The calculations of axially symmetric flow can be simplified if tabulated values of some coefficients of the conical flow are obtained. The method has also been applied to slender bodies without symmetry and to some three-dimensional wing problems where two-dimensional flow can be used as the basic flow. Both problems were unsolved before in the approximation of nonlinear flow.
Modified Cholesky factorizations in interior-point algorithms for linear programming.
Wright, S.; Mathematics and Computer Science
1999-01-01
We investigate a modified Cholesky algorithm typical of those used in most interior-point codes for linear programming. Cholesky-based interior-point codes are popular for three reasons: their implementation requires only minimal changes to standard sparse Cholesky algorithms (allowing us to take full advantage of software written by specialists in that area); they tend to be more efficient than competing approaches that use alternative factorizations; and they perform robustly on most practical problems, yielding good interior-point steps even when the coefficient matrix of the main linear system to be solved for the step components is ill conditioned. We investigate this surprisingly robust performance by using analytical tools from matrix perturbation theory and error analysis, illustrating our results with computational experiments. Finally, we point out the potential limitations of this approach.
Improve Problem Solving Skills through Adapting Programming Tools
NASA Technical Reports Server (NTRS)
Shaykhian, Linda H.; Shaykhian, Gholam Ali
2007-01-01
There are numerous ways for engineers and students to become better problem-solvers. The use of command line and visual programming tools can help to model a problem and formulate a solution through visualization. The analysis of problem attributes and constraints provide insight into the scope and complexity of the problem. The visualization aspect of the problem-solving approach tends to make students and engineers more systematic in their thought process and help them catch errors before proceeding too far in the wrong direction. The problem-solver identifies and defines important terms, variables, rules, and procedures required for solving a problem. Every step required to construct the problem solution can be defined in program commands that produce intermediate output. This paper advocates improved problem solving skills through using a programming tool. MatLab created by MathWorks, is an interactive numerical computing environment and programming language. It is a matrix-based system that easily lends itself to matrix manipulation, and plotting of functions and data. MatLab can be used as an interactive command line or a sequence of commands that can be saved in a file as a script or named functions. Prior programming experience is not required to use MatLab commands. The GNU Octave, part of the GNU project, a free computer program for performing numerical computations, is comparable to MatLab. MatLab visual and command programming are presented here.
New computer program solves wide variety of heat flow problems
NASA Technical Reports Server (NTRS)
Almond, J. C.
1966-01-01
Boeing Engineering Thermal Analyzer /BETA/ computer program uses numerical methods to provide accurate heat transfer solutions to a wide variety of heat flow problems. The program solves steady-state and transient problems in almost any situation that can be represented by a resistance-capacitance network.
Lefkoff, L.J.; Gorelick, S.M.
1987-01-01
A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)
Xia, Youshen; Feng, Gang; Wang, Jun
2004-09-01
This paper presents a recurrent neural network for solving strict convex quadratic programming problems and related linear piecewise equations. Compared with the existing neural networks for quadratic program, the proposed neural network has a one-layer structure with a low model complexity. Moreover, the proposed neural network is shown to have a finite-time convergence and exponential convergence. Illustrative examples further show the good performance of the proposed neural network in real-time applications. PMID:15312842
NASA Technical Reports Server (NTRS)
Pilkey, W. D.; Chen, Y. H.
1974-01-01
An indirect synthesis method is used in the efficient optimal design of multi-degree of freedom, multi-design element, nonlinear, transient systems. A limiting performance analysis which requires linear programming for a kinematically linear system is presented. The system is selected using system identification methods such that the designed system responds as closely as possible to the limiting performance. The efficiency is a result of the method avoiding the repetitive systems analyses accompanying other numerical optimization methods.
NASA Astrophysics Data System (ADS)
Gallagher, Kerry; Sambridge, Malcolm; Drijkoningen, Guy
In providing a method for solving non-linear optimization problems Monte Carlo techniques avoid the need for linearization but, in practice, are often prohibitive because of the large number of models that must be considered. A new class of methods known as Genetic Algorithms have recently been devised in the field of Artificial Intelligence. We outline the basic concept of genetic algorithms and discuss three examples. We show that, in locating an optimal model, the new technique is far superior in performance to Monte Carlo techniques in all cases considered. However, Monte Carlo integration is still regarded as an effective method for the subsequent model appraisal.
Linear Stability of Elliptic Lagrangian Solutions of the Planar Three-Body Problem via Index Theory
NASA Astrophysics Data System (ADS)
Hu, Xijun; Long, Yiming; Sun, Shanzhong
2014-09-01
It is well known that the linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three-body problem depends on the mass parameter and the eccentricity . We are not aware of any existing analytical method which relates the linear stability of these solutions to the two parameters directly in the full rectangle [0, 9] × [0, 1), aside from perturbation methods for e > 0 small enough, blow-up techniques for e sufficiently close to 1, and numerical studies. In this paper, we introduce a new rigorous analytical method to study the linear stability of these solutions in terms of the two parameters in the full ( β, e) range [0, 9] × [0, 1) via the ω-index theory of symplectic paths for ω belonging to the unit circle of the complex plane, and the theory of linear operators. After establishing the ω-index decreasing property of the solutions in β for fixed , we prove the existence of three curves located from left to right in the rectangle [0, 9] × [0, 1), among which two are -1 degeneracy curves and the third one is the right envelope curve of the ω-degeneracy curves, and show that the linear stability pattern of such elliptic Lagrangian solutions changes if and only if the parameter ( β, e) passes through each of these three curves. Interesting symmetries of these curves are also observed. The linear stability of the singular case when the eccentricity e approaches 1 is also analyzed in detail.
Development and validation of a general purpose linearization program for rigid aircraft models
NASA Technical Reports Server (NTRS)
Duke, E. L.; Antoniewicz, R. F.
1985-01-01
A FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft models is discussed. The program LINEAR numerically determines a linear systems model using nonlinear equations of motion and a user-supplied, nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model. Also, included in the report is a comparison of linear and nonlinear models for a high performance aircraft.
ERIC Educational Resources Information Center
Kim, SugHee; Chung, KwangSik; Yu, HeonChang
2013-01-01
The purpose of this paper is to propose a training program for creative problem solving based on computer programming. The proposed program will encourage students to solve real-life problems through a creative thinking spiral related to cognitive skills with computer programming. With the goal of enhancing digital fluency through this proposed…
Warid, Warid; Hizam, Hashim; Mariun, Norman; Abdul-Wahab, Noor Izzri
2016-01-01
This paper proposes a new formulation for the multi-objective optimal power flow (MOOPF) problem for meshed power networks considering distributed generation. An efficacious multi-objective fuzzy linear programming optimization (MFLP) algorithm is proposed to solve the aforementioned problem with and without considering the distributed generation (DG) effect. A variant combination of objectives is considered for simultaneous optimization, including power loss, voltage stability, and shunt capacitors MVAR reserve. Fuzzy membership functions for these objectives are designed with extreme targets, whereas the inequality constraints are treated as hard constraints. The multi-objective fuzzy optimal power flow (OPF) formulation was converted into a crisp OPF in a successive linear programming (SLP) framework and solved using an efficient interior point method (IPM). To test the efficacy of the proposed approach, simulations are performed on the IEEE 30-busand IEEE 118-bus test systems. The MFLP optimization is solved for several optimization cases. The obtained results are compared with those presented in the literature. A unique solution with a high satisfaction for the assigned targets is gained. Results demonstrate the effectiveness of the proposed MFLP technique in terms of solution optimality and rapid convergence. Moreover, the results indicate that using the optimal DG location with the MFLP algorithm provides the solution with the highest quality. PMID:26954783
Warid, Warid; Hizam, Hashim; Mariun, Norman; Abdul-Wahab, Noor Izzri
2016-01-01
This paper proposes a new formulation for the multi-objective optimal power flow (MOOPF) problem for meshed power networks considering distributed generation. An efficacious multi-objective fuzzy linear programming optimization (MFLP) algorithm is proposed to solve the aforementioned problem with and without considering the distributed generation (DG) effect. A variant combination of objectives is considered for simultaneous optimization, including power loss, voltage stability, and shunt capacitors MVAR reserve. Fuzzy membership functions for these objectives are designed with extreme targets, whereas the inequality constraints are treated as hard constraints. The multi-objective fuzzy optimal power flow (OPF) formulation was converted into a crisp OPF in a successive linear programming (SLP) framework and solved using an efficient interior point method (IPM). To test the efficacy of the proposed approach, simulations are performed on the IEEE 30-busand IEEE 118-bus test systems. The MFLP optimization is solved for several optimization cases. The obtained results are compared with those presented in the literature. A unique solution with a high satisfaction for the assigned targets is gained. Results demonstrate the effectiveness of the proposed MFLP technique in terms of solution optimality and rapid convergence. Moreover, the results indicate that using the optimal DG location with the MFLP algorithm provides the solution with the highest quality. PMID:26954783
Decomposition and (importance) sampling techniques for multi-stage stochastic linear programs
Infanger, G.
1993-11-01
The difficulty of solving large-scale multi-stage stochastic linear programs arises from the sheer number of scenarios associated with numerous stochastic parameters. The number of scenarios grows exponentially with the number of stages and problems get easily out of hand even for very moderate numbers of stochastic parameters per stage. Our method combines dual (Benders) decomposition with Monte Carlo sampling techniques. We employ importance sampling to efficiently obtain accurate estimates of both expected future costs and gradients and right-hand sides of cuts. The method enables us to solve practical large-scale problems with many stages and numerous stochastic parameters per stage. We discuss the theory of sharing and adjusting cuts between different scenarios in a stage. We derive probabilistic lower and upper bounds, where we use importance path sampling for the upper bound estimation. Initial numerical results turned out to be promising.
Kim, D.; Ghanem, R.
1994-12-31
Multigrid solution technique to solve a material nonlinear problem in a visual programming environment using the finite element method is discussed. The nonlinear equation of equilibrium is linearized to incremental form using Newton-Rapson technique, then multigrid solution technique is used to solve linear equations at each Newton-Rapson step. In the process, adaptive mesh refinement, which is based on the bisection of a pair of triangles, is used to form grid hierarchy for multigrid iteration. The solution process is implemented in a visual programming environment with distributed computing capability, which enables more intuitive understanding of solution process, and more effective use of resources.
Evaluation of boundary element methods for the EEG forward problem: Effect of linear interpolation
Schlitt, H.A.; Heller, L.; Best, E.; Ranken, D.M. ); Aaron, R. )
1995-01-01
We implement the approach for solving the boundary integral equation for the electroencephalography (EEG) forward problem proposed by de Munck, in which the electric potential varies linearly across each plane triangle of the mesh. Previous solutions have assumed the potential is constant across an element. We calculate the electric potential and systematically investigate the effect of different mesh choices and dipole locations by using a three concentric sphere head model for which there is an analytic solution. Implementing the linear interpolation approximation results in errors that are approximately half those of the same mesh when the potential is assumed to be constant, and provides a reliable method for solving the problem. 12 refs., 8 figs.
Solution of second order quasi-linear boundary value problems by a wavelet method
Zhang, Lei; Zhou, Youhe; Wang, Jizeng
2015-03-10
A wavelet Galerkin method based on expansions of Coiflet-like scaling function bases is applied to solve second order quasi-linear boundary value problems which represent a class of typical nonlinear differential equations. Two types of typical engineering problems are selected as test examples: one is about nonlinear heat conduction and the other is on bending of elastic beams. Numerical results are obtained by the proposed wavelet method. Through comparing to relevant analytical solutions as well as solutions obtained by other methods, we find that the method shows better efficiency and accuracy than several others, and the rate of convergence can even reach orders of 5.8.
The conjugate gradient method for linear ill-posed problems with operator perturbations
NASA Astrophysics Data System (ADS)
Plato, Robert
1999-03-01
We consider an ill-posed problem Ta = f* in Hilbert spaces and suppose that the linear bounded operator T is approximately available, with a known estimate for the operator perturbation at the solution. As a numerical scheme the CGNR-method is considered, that is, the classical method of conjugate gradients by Hestenes and Stiefel applied to the associated normal equations. Two a posteriori stopping rules are introduced, and convergence results are provided for the corresponding approximations, respectively. As a specific application, a parameter estimation problem is considered.
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Rosen, I. G.
1985-01-01
In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Rosen, I. G.
1987-01-01
In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.
Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H.
1996-12-31
The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.
A Conforming Multigrid Method for the Pure Traction Problem of Linear Elasticity: Mixed Formulation
NASA Technical Reports Server (NTRS)
Lee, Chang-Ock
1996-01-01
A multigrid method using conforming P-1 finite element is developed for the two-dimensional pure traction boundary value problem of linear elasticity. The convergence is uniform even as the material becomes nearly incompressible. A heuristic argument for acceleration of the multigrid method is discussed as well. Numerical results with and without this acceleration as well as performance estimates on a parallel computer are included.
A linear-quadratic-Gaussian control problem with innovations-feedthrough solution
NASA Technical Reports Server (NTRS)
Platzman, L. K.; Johnson, T. L.
1976-01-01
The structure of the separation-theorem solution to the standard linear-quadratic-Gaussian (LQG) control problem does not involve direct output feedback as a consequence of the form of the performance index. It is shown that the performance index may be generalized in a natural fashion so that the optimal control law involves output feedback or, equivalently, innovations feedthrough (IF). Applications where this formulation may be advantageous are indicated through an examination of properties of the IF control law.
NASA Technical Reports Server (NTRS)
Ito, K.; Teglas, R.
1984-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
NASA Technical Reports Server (NTRS)
Ito, Kazufumi; Teglas, Russell
1987-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
NASA Technical Reports Server (NTRS)
Arneson, Heather M.; Dousse, Nicholas; Langbort, Cedric
2014-01-01
We consider control design for positive compartmental systems in which each compartment's outflow rate is described by a concave function of the amount of material in the compartment.We address the problem of determining the routing of material between compartments to satisfy time-varying state constraints while ensuring that material reaches its intended destination over a finite time horizon. We give sufficient conditions for the existence of a time-varying state-dependent routing strategy which ensures that the closed-loop system satisfies basic network properties of positivity, conservation and interconnection while ensuring that capacity constraints are satisfied, when possible, or adjusted if a solution cannot be found. These conditions are formulated as a linear programming problem. Instances of this linear programming problem can be solved iteratively to generate a solution to the finite horizon routing problem. Results are given for the application of this control design method to an example problem. Key words: linear programming; control of networks; positive systems; controller constraints and structure.
A linear programming model for reducing system peak through customer load control programs
Kurucz, C.N.; Brandt, D.; Sim, S.
1996-11-01
A Linear Programming (LP) model was developed to optimize the amount of system peak load reduction through scheduling of control periods in commercial/industrial and residential load control programs at Florida Power and Light Company. The LP model can be used to determine both long and short term control scheduling strategies and for planning the number of customers which should be enrolled in each program. Results of applying the model to a forecasted late 1990s summer peak day load shape are presented. It is concluded that LP solutions provide a relatively inexpensive and powerful approach to planning and scheduling load control. Also, it is not necessary to model completely general scheduling of control periods in order to obtain near best solutions to peak load reduction.
Robust parallel iterative solvers for linear and least-squares problems, Final Technical Report
Saad, Yousef
2014-01-16
The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners for solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the
Sun Wei; Huang, Guo H.; Lv Ying; Li Gongchen
2012-06-15
Highlights: Black-Right-Pointing-Pointer Inexact piecewise-linearization-based fuzzy flexible programming is proposed. Black-Right-Pointing-Pointer It's the first application to waste management under multiple complexities. Black-Right-Pointing-Pointer It tackles nonlinear economies-of-scale effects in interval-parameter constraints. Black-Right-Pointing-Pointer It estimates costs more accurately than the linear-regression-based model. Black-Right-Pointing-Pointer Uncertainties are decreased and more satisfactory interval solutions are obtained. - Abstract: To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP's advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate
Solving Integer Programming Problems by Using Artificial Bee Colony Algorithm
NASA Astrophysics Data System (ADS)
Akay, Bahriye; Karaboga, Dervis
This paper presents a study that applies the Artificial Bee Colony algorithm to integer programming problems and compares its performance with those of Particle Swarm Optimization algorithm variants and Branch and Bound technique presented to the literature. In order to cope with integer programming problems, in neighbour solution production unit, solutions are truncated to the nearest integer values. The experimental results show that Artificial Bee Colony algorithm can handle integer programming problems efficiently and Artificial Bee Colony algorithm can be considered to be very robust by the statistics calculated such as mean, median, standard deviation.
Measurement problem in Program Universe. Revision
Noyes, H.P.; Gefwert, C.; Manthey, M.J.
1985-07-01
The ''measurement problem'' of contemporary physics is in our view an artifact of its philosophical and mathematical underpinnings. We describe a new philosophical view of theory formation, rooted in Wittgenstein, and Bishop's and Martin-Loef's constructivity, which obviates such discussions. We present an unfinished, but very encouraging, theory which is compatible with this philosophical framework. The theory is based on the concepts of counting and combinatorics in the framework provided by the combinatorial hierarchy, a unique hierarchy of bit strings which interact by an operation called discrimination. Measurement criteria incorporate c, h-bar and m/sub p/ or (not ''and'') G. The resulting theory is discrete throughout, contains no infinities, and, as far as we have developed it, is in agreement with quantum mechanical and cosmological fact. 15 refs.
Two Computer Programs for the Statistical Evaluation of a Weighted Linear Composite.
ERIC Educational Resources Information Center
Sands, William A.
1978-01-01
Two computer programs (one batch, one interactive) are designed to provide statistics for a weighted linear combination of several component variables. Both programs provide mean, variance, standard deviation, and a validity coefficient. (Author/JKS)
NASA Astrophysics Data System (ADS)
Veera Raghavan, Srikant
Semidefinite programming (SDP) is a relatively modern subfield of convex optimization which has been applied to many problems in the reduced density matrix (RDM) formulation of electronic structure. SDPs deal with minimization (or maximization) of linear objective functions of matrices, subject to linear equality and inequality constraints and positivity constraints on the eigenvalues of the matrices. Energies of chemical systems can be expressed as linear functions of RDMs, whose eigenvalues are electron occupation numbers or their products which are expected to be non-negative. Therefore, it is perhaps not surprising that SDPs fit rather naturally in the RDM framework in electronic structure. This dissertation presents SDP applications to two electronic structure theories. The first part of this dissertation (chaps. 1-3) reformulates Hartree-Fock theory in terms of SDPs in order to obtain upper and lower bounds to global Hartree-Fock energies. The upper and lower bounds on the energies are frequently equal thereby providing a first-ever certificate of global optimality for many Hartree-Fock solutions. The SDP approach provides an alternative to the conventional self-consistent field method of obtaining Hartree-Fock energies and densities with the added benefit of global optimality or a rigorous lower bound. Applications are made to the potential energy curves of (H 4)2, N2, C2, CN, Cr2 and NO2. Energies of the first-row transition elements are also calculated. In chapter 4, the effect of using the Hartree-Fock solutions that we calculate as references for coupled cluster singles doubles calculations is presented for some of the above molecules. The second part of this dissertation (chap. 5) presents a SDP approach to electronic structure methods which scale linearly with system size. Linear scaling electronic structure methods are essential in order to make calculations on large systems feasible. Among these methods the so-called density matrix based ones seek to
Symbolic programming language in molecular multicenter integral problem
NASA Astrophysics Data System (ADS)
Safouhi, Hassan; Bouferguene, Ahmed
It is well known that in any ab initio molecular orbital (MO) calculation, the major task involves the computation of molecular integrals, among which the computation of three-center nuclear attraction and Coulomb integrals is the most frequently encountered. As the molecular system becomes larger, computation of these integrals becomes one of the most laborious and time-consuming steps in molecular systems calculation. Improvement of the computational methods of molecular integrals would be indispensable to further development in computational studies of large molecular systems. To develop fast and accurate algorithms for the numerical evaluation of these integrals over B functions, we used nonlinear transformations for improving convergence of highly oscillatory integrals. These methods form the basis of new methods for solving various problems that were unsolvable otherwise and have many applications as well. To apply these nonlinear transformations, the integrands should satisfy linear differential equations with coefficients having asymptotic power series in the sense of Poincaré, which in their turn should satisfy some limit conditions. These differential equations are very difficult to obtain explicitly. In the case of molecular integrals, we used a symbolic programming language (MAPLE) to demonstrate that all the conditions required to apply these nonlinear transformation methods are satisfied. Differential equations are obtained explicitly, allowing us to demonstrate that the limit conditions are also satisfied.
NASA Technical Reports Server (NTRS)
Wei, Peng; Sridhar, Banavar; Chen, Neil Yi-Nan; Sun, Dengfent
2012-01-01
A class of strategies has been proposed to reduce contrail formation in the United States airspace. A 3D grid based on weather data and the cruising altitude level of aircraft is adjusted to avoid the persistent contrail potential area with the consideration to fuel-efficiency. In this paper, the authors introduce a contrail avoidance strategy on 3D grid by considering additional operationally feasible constraints from an air traffic controller's aspect. First, shifting too many aircraft to the same cruising level will make the miles-in-trail at this level smaller than the safety separation threshold. Furthermore, the high density of aircraft at one cruising level may exceed the workload for the traffic controller. Therefore, in our new model we restrict the number of total aircraft at each level. Second, the aircraft count variation for successive intervals cannot be too drastic since the workload to manage climbing/descending aircraft is much larger than managing cruising aircraft. The contrail reduction is formulated as an integer-programming problem and the problem is shown to have the property of total unimodularity. Solving the corresponding relaxed linear programming with the simplex method provides an optimal and integral solution to the problem. Simulation results are provided to illustrate the methodology.
LQR problem of linear discrete time systems with nonnegative state constraints
NASA Astrophysics Data System (ADS)
Kostova, S.; Imsland, L.; Ivanov, I.
2015-10-01
In the paper the infinite-horizon Linear Quadratic Regulator (LQR) problem of linear discrete time systems with non-negative state constraints is presented. Such kind of constraints on the system determine the class of positive systems. They have big application in many fields like economics, biology, ecology, ICT and others. The standard infinite LQR-optimal state feedback law is used for solving the problem. In order to guarantee the nonnegativity of the system states, we define the admissible set of initial states. It is proven that, for each initial state from this set the nonnegative orthant is invariant set. Two cases are considered, first, when the initial state belongs to the admissible set, and the second, when the initial state does not belong to the admissible set. The procedures for solving the problem are given for two cases. In second case we use a dual-mode approach for solving the problem. The first mode is until the state trajectory enters the admissible set and after that the procedure for the first case is used. The illustrative examples are given for both cases.
DRIESSEN,BRIAN; SADEGH,NADER
2000-04-25
This work presents a method of finding near global optima to minimum-time trajectory generation problem for systems that would be linear if it were not for the presence of Coloumb friction. The required final state of the system is assumed to be maintainable by the system, and the input bounds are assumed to be large enough so that they can overcome the maximum static Coloumb friction force. Other than the previous work for generating minimum-time trajectories for non redundant robotic manipulators for which the path in joint space is already specified, this work represents, to the best of the authors' knowledge, the first approach for generating near global optima for minimum-time problems involving a nonlinear class of dynamic systems. The reason the optima generated are near global optima instead of exactly global optima is due to a discrete-time approximation of the system (which is usually used anyway to simulate such a system numerically). The method closely resembles previous methods for generating minimum-time trajectories for linear systems, where the core operation is the solution of a Phase I linear programming problem. For the nonlinear systems considered herein, the core operation is instead the solution of a mixed integer linear programming problem.
Promising Parenting Programs for Reducing Adolescent Problem Behaviors
Haggerty, Kevin P.; McGlynn-Wright, Anne; Klima, Tali
2013-01-01
Purpose Adolescent problem behaviors (substance use, delinquency, school dropout, pregnancy, and violence) are costly not only for individuals, but for entire communities. Policymakers and practitioners that are interested in preventing these problem behaviors are faced with many programming options. In this review, we discuss two criteria for selecting relevant parenting programs, and provide five examples of such programs. Design/methodology/approach The first criterion for program selection is theory based. Well-supported theories, such as the social development model, have laid out key family-based risk and protective factors for problem behavior. Programs that target these risk and protective factors are more likely to be effective. Second, programs should have demonstrated efficacy; these interventions have been called “evidence-based programs” (EBP). This review highlights the importance of evidence from rigorous research designs, such as randomized clinical trials, in order to establish program efficacy. Findings Nurse-Family Partnership, The Incredible Years, Positive Parenting Program, Strengthening Families 10–14, and Staying Connected with Your Teen are examined. The unique features of each program are briefly presented. Evidence showing impact on family risk and protective factors, as well as long-term problem behaviors, is reviewed. Finally, a measure of cost effectiveness of each program is provided. Originality/value We propose that not all programs are of equal value, and suggest two simple criteria for selecting a parenting program with a high likelihood for positive outcomes. Furthermore, although this review is not exhaustive, the five examples of EBPs offer a good start for policymakers and practitioners seeking to implement effective programs in their communities. Thus, this paper offers practical suggestions for those grappling with investments in child and adolescent programs on the ground. PMID:24416068
A Linear Time Algorithm for the Minimum Spanning Caterpillar Problem for Bounded Treewidth Graphs
NASA Astrophysics Data System (ADS)
Dinneen, Michael J.; Khosravani, Masoud
We consider the Minimum Spanning Caterpillar Problem (MSCP) in a graph where each edge has two costs, spine (path) cost and leaf cost, depending on whether it is used as a spine or a leaf edge. The goal is to find a spanning caterpillar in which the sum of its edge costs is the minimum. We show that the problem has a linear time algorithm when a tree decomposition of the graph is given as part of the input. Despite the fast growing constant factor of the time complexity of our algorithm, it is still practical and efficient for some classes of graphs, such as outerplanar, series-parallel (K 4 minor-free), and Halin graphs. We also briefly explain how one can modify our algorithm to solve the Minimum Spanning Ring Star and the Dual Cost Minimum Spanning Tree Problems.
ERIC Educational Resources Information Center
Schmitt, M. A.; And Others
1994-01-01
Compares traditional manure application planning techniques calculated to meet agronomic nutrient needs on a field-by-field basis with plans developed using computer-assisted linear programming optimization methods. Linear programming provided the most economical and environmentally sound manure application strategy. (Contains 15 references.) (MDH)
Sun, Wei; Huang, Guo H; Lv, Ying; Li, Gongchen
2012-06-01
To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP's advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP's solutions demonstrate its effectiveness for providing more satisfactory interval solutions than IPFP3. Following its first application to waste management, the IPFP can be potentially applied to other environmental problems under multiple complexities. PMID:22370050
Boundary parametric approximation to the linearized scalar potential magnetostatic field problem
Bramble, J.H.; Pasciak, J.E.
1984-01-01
We consider the linearized scalar potential formulation of the magnetostatic field problem in this paper. Our approach involves a reformulation of the continuous problem as a parametric boundary problem. By the introduction of a spherical interface and the use of spherical harmonics, the infinite boundary conditions can also be satisfied in the parametric framework. That is, the field in the exterior of a sphere is expanded in a harmonic series of eigenfunctions for the exterior harmonic problem. The approach is essentially a finite element method coupled with a spectral method via a boundary parametric procedure. The reformulated problem is discretized by finite element techniques which lead to a discrete parametric problem which can be solved by well conditioned iteration involving only the solution of decoupled Neumann type elliptic finite element systems and L/sup 2/ projection onto subspaces of spherical harmonics. Error and stability estimates given show exponential convergence in the degree of the spherical harmonics and optimal order convergence with respect to the finite element approximation for the resulting fields in L/sup 2/. 24 references.
Experiences in Rural Mental Health. VIII: Programming and Administrative Problems.
ERIC Educational Resources Information Center
Hollister, William G.; And Others
Based on a North Carolina Feasibility study (1967-73) which focused on development of a pattern for providing comprehensive mental health services to rural people, this guide deals with programming and administrative problems in Vance and Franklin counties. Describing those problems believed to be most likely to occur in rural areas, this booklet…
Problem Solving Variations in an Online Programming Course
ERIC Educational Resources Information Center
Ebrahimi, Alireza
2007-01-01
An observation on teaching introductory programming courses on SLN for a period of two terms led me to believe that online students try various ways to solve a problem. In the beginning, I got the impression that some of their approaches for a solution were wrong; but after a little investigation, I found that some of the problem-solving…
Acceleration of multiple solution of a boundary value problem involving a linear algebraic system
NASA Astrophysics Data System (ADS)
Gazizov, Talgat R.; Kuksenko, Sergey P.; Surovtsev, Roman S.
2016-06-01
Multiple solution of a boundary value problem that involves a linear algebraic system is considered. New approach to acceleration of the solution is proposed. The approach uses the structure of the linear system matrix. Particularly, location of entries in the right columns and low rows of the matrix, which undergo variation due to the computing in the range of parameters, is used to apply block LU decomposition. Application of the approach is considered on the example of multiple computing of the capacitance matrix by method of moments used in numerical electromagnetics. Expressions for analytic estimation of the acceleration are presented. Results of the numerical experiments for solution of 100 linear systems with matrix orders of 1000, 2000, 3000 and different relations of variated and constant entries of the matrix show that block LU decomposition can be effective for multiple solution of linear systems. The speed up compared to pointwise LU factorization increases (up to 15) for larger number and order of considered systems with lower number of variated entries.
NASA Technical Reports Server (NTRS)
Fleming, P.
1985-01-01
A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.
Problems in Choosing Tools and Methods for Teaching Programming
ERIC Educational Resources Information Center
Vitkute-Adžgauskiene, Davia; Vidžiunas, Antanas
2012-01-01
The paper analyses the problems in selecting and integrating tools for delivering basic programming knowledge at the university level. Discussion and analysis of teaching the programming disciplines, the main principles of study programme design, requirements for teaching tools, methods and corresponding languages is presented, based on literature…
Analytical solution of boundary integral equations for 2-D steady linear wave problems
NASA Astrophysics Data System (ADS)
Chuang, J. M.
2005-10-01
Based on the Fourier transform, the analytical solution of boundary integral equations formulated for the complex velocity of a 2-D steady linear surface flow is derived. It has been found that before the radiation condition is imposed, free waves appear both far upstream and downstream. In order to cancel the free waves in far upstream regions, the eigensolution of a specific eigenvalue, which satisfies the homogeneous boundary integral equation, is found and superposed to the analytical solution. An example, a submerged vortex, is used to demonstrate the derived analytical solution. Furthermore, an analytical approach to imposing the radiation condition in the numerical solution of boundary integral equations for 2-D steady linear wave problems is proposed.
Variable-permittivity linear inverse problem for the H(sub z)-polarized case
NASA Technical Reports Server (NTRS)
Moghaddam, M.; Chew, W. C.
1993-01-01
The H(sub z)-polarized inverse problem has rarely been studied before due to the complicated way in which the unknown permittivity appears in the wave equation. This problem is equivalent to the acoustic inverse problem with variable density. We have recently reported the solution to the nonlinear variable-permittivity H(sub z)-polarized inverse problem using the Born iterative method. Here, the linear inverse problem is solved for permittivity (epsilon) and permeability (mu) using a different approach which is an extension of the basic ideas of diffraction tomography (DT). The key to solving this problem is to utilize frequency diversity to obtain the required independent measurements. The receivers are assumed to be in the far field of the object, and plane wave incidence is also assumed. It is assumed that the scatterer is weak, so that the Born approximation can be used to arrive at a relationship between the measured pressure field and two terms related to the spatial Fourier transform of the two unknowns, epsilon and mu. The term involving permeability corresponds to monopole scattering and that for permittivity to dipole scattering. Measurements at several frequencies are used and a least squares problem is solved to reconstruct epsilon and mu. It is observed that the low spatial frequencies in the spectra of epsilon and mu produce inaccuracies in the results. Hence, a regularization method is devised to remove this problem. Several results are shown. Low contrast objects for which the above analysis holds are used to show that good reconstructions are obtained for both permittivity and permeability after regularization is applied.
On Linear Instability and Stability of the Rayleigh-Taylor Problem in Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Jiang, Fei; Jiang, Song
2015-12-01
We investigate the stabilizing effects of the magnetic fields in the linearized magnetic Rayleigh-Taylor (RT) problem of a nonhomogeneous incompressible viscous magnetohydrodynamic fluid of zero resistivity in the presence of a uniform gravitational field in a three-dimensional bounded domain, in which the velocity of the fluid is non-slip on the boundary. By adapting a modified variational method and careful deriving a priori estimates, we establish a criterion for the instability/stability of the linearized problem around a magnetic RT equilibrium state. In the criterion, we find a new phenomenon that a sufficiently strong horizontal magnetic field has the same stabilizing effect as that of the vertical magnetic field on growth of the magnetic RT instability. In addition, we further study the corresponding compressible case, i.e., the Parker (or magnetic buoyancy) problem, for which the strength of a horizontal magnetic field decreases with height, and also show the stabilizing effect of a sufficiently large magnetic field.
Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer M; Derocher, Andrew E; Lewis, Mark A; Jonsen, Ian D; Mills Flemming, Joanna
2016-01-01
State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results. PMID:27220686
Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer M.; Derocher, Andrew E.; Lewis, Mark A.; Jonsen, Ian D.; Mills Flemming, Joanna
2016-01-01
State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results. PMID:27220686
Using Perturbed QR Factorizations To Solve Linear Least-Squares Problems
Avron, Haim; Ng, Esmond G.; Toledo, Sivan
2008-03-21
We propose and analyze a new tool to help solve sparse linear least-squares problems min{sub x} {parallel}Ax-b{parallel}{sub 2}. Our method is based on a sparse QR factorization of a low-rank perturbation {cflx A} of A. More precisely, we show that the R factor of {cflx A} is an effective preconditioner for the least-squares problem min{sub x} {parallel}Ax-b{parallel}{sub 2}, when solved using LSQR. We propose applications for the new technique. When A is rank deficient we can add rows to ensure that the preconditioner is well-conditioned without column pivoting. When A is sparse except for a few dense rows we can drop these dense rows from A to obtain {cflx A}. Another application is solving an updated or downdated problem. If R is a good preconditioner for the original problem A, it is a good preconditioner for the updated/downdated problem {cflx A}. We can also solve what-if scenarios, where we want to find the solution if a column of the original matrix is changed/removed. We present a spectral theory that analyzes the generalized spectrum of the pencil (A*A,R*R) and analyze the applications.
On the classical solution to the linear-constrained minimum energy problem
NASA Astrophysics Data System (ADS)
Boissaux, Marc; Schiltz, Jang
2012-02-01
Minimum energy problems involving linear systems with quadratic performance criteria are classical in optimal control theory. The case where controls are constrained is discussed in Athans and Falb (1966) [Athans, M. and Falb, P.L. (1966), Optimal Control: An Introduction to the Theory and Its Applications, New York: McGraw-Hill Book Co.] who obtain a componentwise optimal control expression involving a saturation function expression. We show why the given expression is not generally optimal in the case where the dimension of the control is greater than one and provide a numerical counterexample.
Short communication : a linear assignment approach for the least-squares protein morphing problem.
Anitescu, M.; Park, S.; Mathematics and Computer Science
2009-02-01
This work addresses the computation of free-energy differences between protein conformations by using morphing (i.e., transformation) of a source conformation into a target conformation. To enhance the morphing procedure, we employ permutations of atoms: we seek to find the permutation s that minimizes the mean-square distance traveled by the atoms. Instead of performing this combinatorial search in the space of permutations, we show that the best permutation can be found by solving a linear assignment problem. We demonstrate that the use of such optimal permutations significantly improves the efficiency of the free-energy computation.
Programmable calculator program for linear somatic cell scores to estimate mastitis yield losses.
Kirk, J H
1984-02-01
A programmable calculator program calculates loss of milk yield in dairy cows based on linear somatic cell count scores. The program displays the distribution of the herd by lactation number and linear score for present and optimal goal situations. Loss of yield is in pounds and dollars by cow and herd. The program estimates optimal milk production and numbers of fewer cows at the goal for mastitis infection. PMID:6546938
Leontidis, S; Fernández, A; Rodrigo, C; Fernández, P S; Magraner, L; Martínez, A
1999-08-01
A systematic study of the inactivation kinetics of Bacillus stearothermophilus spores was carried out in nonisothermic heating conditions using a linear temperature increase program and analyzing the experimental data by means of a one-step nonlinear regression. The D and z values estimated are close to those obtained in isothermic conditions and estimated by using a two-step model, first D values are calculated, and then in the second step a z value is deduced (D(121 degrees C) = 3.08 and 4.38 min, respectively, and z = 7 and 7.9 degrees C, respectively). No convergence problems were observed when using the one-step nonlinear regression proposed. The results indicated that the methodology applied in this study can be used to obtain kinetic data for bacterial spores, which could mean a significant reduction in the amount of experimental work employed to generate these data. PMID:10456754