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SATISFYING SOLUTIONS FOR A POSSIBILISTIC linear PROGRAM

INFORMATION SCIENCES 1986年第3期40卷 247-265页

作者： LUHANDJULA, MK Institut d"Informatique Université de Tizi-Ouzou Tizi-Ouzou Algeria

A branch and bound scheme is described for tackling a linear program under discrete possibilistic data. We grapple also with the continuous case via recent results on inexact and semiinfinite programming. It is shown that solutions yielded by these techniques are satisfying, i.e. possibly and/or necessarily feasible, and optimal to a great extent. Finally, approaches reported here and elsewhere are appraised in the light of their decision-making philosophies, and some directions for further developments indicated.

关键词： mathematical programming, linear

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ONE-DIMENSIONAL SIMPLEX SEARCH

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COMPUTERS & OPERATIONS RESEARCH 1987年第1期14卷 47-54页

作者： CHOO, E KIM, CH UNIV SANTA CLARA LEAVEY SCHSANTA CLARACA 95053

The simplex search method is known as one of the most robust and efficient direct search methods of optimizing unconstrained multivariate functions. Here, a one-dimensional simplex search is provided that offers some beneficial theoretical and computational properties. For example, the algorithm can start with any 2 points and converges to the optimum of any unimodal function. With appropriate parameters, the algorithm may be made to behave equivalent to some of the most efficient one-dimensional search methods, including the Golden Section method and the binary search method. The simplex search should be quite robust and is an efficient dimensional search algorithm that may be incorporated into a general multidimensional optimization algorithm that calls for such a one-dimensional algorithm whenever the search direction changes.

关键词： mathematical programming, linear

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OBJECTIVE FUNCTION BOUNDS FOR THE INEXACT linear-programming PROBLEM WITH GENERALIZED COST COEFFICIENTS

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COMPUTERS & OPERATIONS RESEARCH 1985年第5期12卷 483-491页

作者： BARD, JF CHATTERJEE, S NORTHEASTERN UNIV COLL BUSINESS ADMBOSTONMA 02115

Most realistic resource allocation problems are such that input, output, and cost coefficients are rarely known with certainty. Therefore, the coefficients must be estimated from available data. The problem of inexact linear programming in which the objective function coefficients are not fixed is addressed. Theoretical results are presented for the best and worst cases, and simulation is used to examine those in between. A wide range of configurations is examined. It is statistically demonstrated that the variance of objective function values is proportional to the size and shape of some predetermined set. The analysis provides a means of addressing linear programming problems with inexact data. Also, the analysis demonstrates how the leverage associated with specific parameters can be identified and exploited to greatest advantage.

关键词： mathematical programming, linear

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INTEGRABILITY OF VECTOR AND MULTIVECTOR FIELDS ASSOCIATED WITH INTERIOR POINT METHODS FOR linear-programming

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mathematical programming 1991年第3期52卷 511-525页

作者： IRI, M 1. Department of Mathematical Engineering and Information Physics Faculty of Engineering University of Tokyo Bunkyo-ku 113 Tokyo Japan

In the feasible region of a linear programming problem, a number of "desirably good" directions have been defined in connexion with various interior point methods. Each of them determines a contravariant vector field in the region whose only stable critical point is the optimum point. Some interior point methods incorporate a two- or higher-dimensional search, which naturally leads us to the introduction of the corresponding contravariant multivector field. We investigate the integrability of those multivector fields, i.e., whether a contravariant p-vector field is X(p)-forming, is enveloped by a family of X(q)'s (q > p) or envelops a family of X(q)'s (q < p) (in J.A. Schouten's terminology), where X(q) is a q-dimensional manifold. Immediate consequences of known facts are: (1) The directions hitherto proposed are X1-forming with the optimum point of the linear programming problem as the stable accumulation point, and (2) there is an X2-forming contravariant bivector field for which the center path is the critical submanifold. Most of the meaningful p-vector fields with p greater-than-or-equal-to 3 are not X(p)-forming in general, though they envelop that bivector field. This observation will add another circumstantial evidence that the bivector field has a kind of invariant significance in the geometry of interior point methods for linear programming. For a kind of appendix, it is noted that, if we have several objectives, i.e., in the case of multiobjective linear programming extension to higher dimensions is easily obtained.

关键词： mathematical programming, linear

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ANALOG-COMPUTER SOLUTION OF CERTAIN ZERO-ONE INTEGER programming-PROBLEMS

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INTERNATIONAL JOURNAL OF ELECTRONICS 1979年第6期46卷 555-561页

作者： ULA, N

This article investigates the possibilities of solving certain zero-one integer programming problems on an analogue computer. It is shown that, excepting the cases where the variables with equal weights in the objective function are constrained with each other, the gradient search technique with suitable modifications yields unique and straightforward solutions for set covering, set partitioning and weighted matching problems. Experimental results are presented and discussed to illustrate the concepts involved.

关键词： mathematical programming, linear

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GENERALIZED EUCLIDEAN PROCEDURE FOR INTEGER linear PROGRAMS

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NAVAL RESEARCH LOGISTICS 1974年第1期21卷 125-144页

作者： RICHMOND, TR RAVINDRAN, A HOWARD UNIV GRAD SCH BUSINESS WASHINGTON DC USA PURDUE UNIV SCH IND ENGN LAFAYETTE IN USA

This paper investigates a new procedure for solving the general-variable pure integer linear programming problem. A simple transformation converts the problem to one of constructing nonnegative integer solutions to a system of linear diophantine equations. Rubin's sequential algorithm, an extension of the classic Euclidean algorithm, is used to find an integer solution to this system of equations. Two new theorems are proved on the properties of integer solutions to linear systems. This permits a modified Fourier-Motzkin elimination method to be used to construct a nonnegative integer solution. An experimental computer code was developed for the algorithm to solve some test problems selected from the literature. The computational results, though limited, are encouraging when compared with the R. E. Gomory all-integer algorithm.

关键词： mathematical programming, linear

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IMPLEMENTATION OF SUCCESSIVE linear-programming ALGORITHMS FOR NON-CONVEX GOAL programming

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COMPUTERS & OPERATIONS RESEARCH 1988年第1期15卷 37-49页

作者： ARMSTRONG, R CHARNES, A HAKSEVER, C BOSTON COLL SCH MANAGEMENTCHESTNUT HILLMA 02167 UNIV TEXAS CTR CYBERNET STUDIESAUSTINTX 78712

Presentation is made of a computer implementation of an effective approach for the solution of nonlinear, nonconvex ratio goals problems. The approach employs Charnes and Cooper's (1977) linearization method of solution of ratio goals problems with a sequence of perturbed linear programming (LP) problems. For efficient solution, it incorporates the Opposite Sign Algorithm and the Negative Image Method, both of which employ the available information from the most recently solved problem. The efficiency of these algorithms against a new start every time a new LP problem is set up for solution has been confirmed by computational testing on randomly generated problems.

关键词： mathematical programming, linear

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RECURRENT NEURAL NETWORKS FOR linear-programming - ANALYSIS AND DESIGN PRINCIPLES

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COMPUTERS & OPERATIONS RESEARCH 1992年第3-4期19卷 297-311页

作者： WANG, J CHANKONG, V CASE WESTERN RESERVE UNIV CLEVELANDOH 44106

This paper explores the potential role of recurrent neural networks for solving linear programs. The emphases of the paper are on analyzing the asymptotic properties of recurrent neural networks that are relevant to linear programming and on developing general principles for designing such neural networks. A class of recurrent neural networks with monotonically increasing penalty variables is presented for solving linear programming problems. The proposed recurrent neural networks are asymptotically stable and able to generate optimal solutions to linear programming problems. The asymptotic properties of the proposed recurrent neural networks for linear programming are analyzed theoretically, and the design principles for synthesizing the recurrent networks are discussed based on the results of analysis. Some illustrative examples are also presented to demonstrate the performance behavior and operational characteristics of the recurrent neural networks.

关键词： mathematical programming, linear

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METHOD FOR THE SOLUTION OF THE linear-programming PROBLEM

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CYBERNETICS 1984年第4期20卷 549-555页

作者： TUNIEV, AD

The author considers a method for the solution of the linear programming problem which chooses, not a single element as in the simplex method, but simultaneously several elements - a whole pivotal vector. The algebraic foundation of the proposed method is provided by the generalized elimination procedure which in each iteration eliminates one group of vectors from a pseudobasis of linearly independent vector and substitutes another group of vectors in its place. Geometrically, the method enables one to move toward the optimum over adjacent faces of different dimensionalities which are defined by the constraints of the linear programming problem.

关键词： mathematical programming, linear

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SOME PROPERTIES OF A CLASS OF CONTINUOUS linear-PROGRAMS

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1983年第5期21卷 758-765页

作者： ANDERSON, EJ NASH, P PEROLD, AF HARVARD UNIV GRAD SCH BUSINESS ADMBOSTONMA 02115

This paper discusses a class of linear programs posed in a function space; a member of this class is called a separated continuous linear program (SCLP). Such problems occur, for example, in the planning of production and inventory. We characterize the $L_\infty $ extreme point solutions of SCLP in a manner analogous to the basic solutions of finite dimensional linear programming and give a sufficient condition for there to exist optimal extreme point solutions with finitely many constant-basis intervals. SCLP is to date the most general continuous linear program for which such strong characterizations have been found.

关键词： mathematical programming, linear

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