Showing papers on "Linear-fractional programming published in 1980"
2,032 citations
TL;DR: It is established that in the worst case, the computational effort required for solving a parametric linear program is not bounded above by a polynomial in the size of the problem.
Abstract: We establish that in the worst case, the computational effort required for solving a parametric linear program is not bounded above by a polynomial in the size of the problem.
146 citations
TL;DR: A sufficient condition for optimality is presented 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.
Abstract: 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. This paper presents 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. Computational results are reported to indicate the efficiency of this approach.
102 citations
01 Jan 1980
TL;DR: An economic interpretation is given and properties of the fuzzy dual problems are derived, leading to a pair of “fuzzy dual” optimization problems.
Abstract: In classical duality theory of linear programming the saddlepoint of the Lagrangian is the solution of the max-min problem as well as of the min-max problem. In using the theory of fuzzy sets these problems are interpreted in a new sense — leading to a pair of “fuzzy dual” optimization problems. An economic interpretation is given and properties of the fuzzy dual problems are derived.
74 citations
TL;DR: L. G. Khachiyan's polynomial time algorithm for determining whether a system of linear inequalities is satisfiable is presented together with a proof of its validity and can be used to solve linear programs in polynometric time.
71 citations
TL;DR: A notion of LP-completeness is introduced, a set of problems is shown to be (polynomially) equivalent to linear programming, and a transformation is given to produce NP-complete versions ofLP-complete provlems.
51 citations
TL;DR: The algorithm can be used to solve the constrained 11 approximation problem and, if no vector x satisfying (2) and (3) exists, the subroutine detects this and informs the user that the problem is infeasible.
Abstract: subject to the given constraints (2) and (3). (In expression (4), b, denotes the ith component of b and A, denotes the ith row of A.) The method is completely general in the sense that no restrictions are imposed on the ranks of the matrices A, C, and E, or on the signs of the elements of f. Furthermore, if no vector x satisfying (2) and (3) exists, the subroutine detects this and informs the user that the problem is infeasible. The algorithm can be used to solve the constrained 11 approximation problem. Suppose that data consisting of k points (t , y,) are to be approximated by a linear
48 citations
TL;DR: It is shown how the ordmal priomty factors m the goal programmmg objective function can be used to partmon the goal constraints of the problem, allowing a sequence of smaller subproblems to be solved in order to fred a solution to the original problem.
Abstract: An algorithm Is presented for solving the hnear goal programming problem It is shown how the ordmal priomty factors m the goal programmmg objective function can be used to partmon the goal constraints of the problem, allowing a sequence of smaller subproblems to be solved in order to fred a solution to the original problem. Also discussed is the additional efficiency of the algorithm achieved by the use of variable elnninatmn and special terminatmn rules. Prehminary computatmnal results demonstrate the efficiency of the new algorithm.
45 citations
TL;DR: A duality theory for generalized linear programs which parallels the usual duality results for linear programming is presented and the duals are a form of inexact linear programs and can be solved by the simplex method.
Abstract: This paper presents a duality theory for generalized linear programs which parallels the usual duality results for linear programming. The duals are a form of inexact linear programs and can be solved by the simplex method. Computational methods with examples and applications are given.
43 citations
TL;DR: A technique for compressing networks is developed that is applicable to any large network, part of a network and to multi-fragnet networks, and its ability to solve the time-cost trade off problems for overlapping precedence networks.
Abstract: A technique for compressing networks is developed. The reduction of project duration, keeping the additional total cost a minimum, is achieved by a cost optimization linear programming model formulated from a chain-bar chart. The final solution is obtained using the computer. The method is applicable to any large network, part of a network and to multi-fragnet networks. The main advantage of this technique is its ability to solve the time-cost trade off problems for overlapping precedence networks. The additional cost of crashing any particular activity is obtained by making the assumption that the cost slope is linear between normal and crash points in the cost-duration curve. The method is simple and of low computational cost.
34 citations
TL;DR: This variant of the piecewise-linear penalty-function approach to linear programming makes use of computational techniques which are more closely related to those in existing computer codes for linear programming and which can be more readily adapted for large sparse problems that were the techniques described by Conn.
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01 Jan 1980
TL;DR: These methods are based on the large-scale programming techniques of decomposition, partitioning, and basic factorization and show conditions under which the stochastic program need not be solved.
Abstract: : Linear programs have been formulated for many practical situations that require decisions made periodically through time. These dynamic linear programs often involve uncertainties. Deterministic solutions of these problems may lead to costly incorrect decisions, and, when a stochastic solution is attempted the problem may become too large. In this report, we present methods for reducing the computational cost of these stochastic programs, and we show conditions under which the stochastic program need not be solved. Our methods are based on the large-scale programming techniques of decomposition, partitioning, and basic factorization. (Author)
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01 Jan 1980
TL;DR: In this article, an interactive algorithm for multicriteria decision-making is presented, which is based on multi-objective linear programming (MLP) and subjective programming.
Abstract: "Characterization of Pareto and Lexicographic Optimal Solutions".- "Duality Based Characterizations of Efficient Facets".- "Sensitivity Analysis in Multiple Objective Linear Programming: Changes in the Objective Function Matrix".- "Exhaustible Resources and a Leontief Model of Production with Scarce Energy".- "Multicriteria Decision Models with Specified Goal Levels".- "Multiple Objective Linear Programming and the Tradeoff - Compromise Set".- "A Note on Size Reduction of the Objective Functions Matrix in Vector Maximum Problems".- "The Surrogate Worth Trade-Off (SWT) Method and its Extensions".- "Bicriterion Path Problems".- "The Haar Condition in Vector Optimization".- "A Comparative Evaluation of Conjoint Measurement and Goal Programming as Aids in Decision Making for Marine Environmental Protection".- "An Experiment with Some Algorithms for Multiple Criteria Decision Making".- "How to Order three Hypotheses According to their Plausibility".- "A Bargaining Model for Solving the Multiple Criteria Problem".- "On Computing the Set of all Weakly Efficient Vertices in Multiple Objective Linear Fractional Programming".- "Multiple Goal Operations Management Planning and Decision Making in a Quality Control Department".- "A Multiple Criteria Analysis Model for Academic Policies, Priorities, and Budgetary Constraints".- "Flexibility and Rigidity in Multicriterion Linear Programming".- "Subjective Programming in Multi-Criterion Decision Making".- "Linear Regression Using Multiple-Criteria".- "Interactive Multiple Goal Programming: an Evaluation and Some Results".- "Psychological Factors in Decision Making: New Decision Models".- "Using Preference Information in Multistep Methods for Solving Multiple Criteria Decision Problems".- "Manpower Allocation with Multiple Objectives - The Min Max Approach".- "Multicriteria Decision-Aid-Making in Production-Management Problems".- "The Use of Local-Global Mapping Techniques in Analysing Multi Criteria Decision Making".- "A Satisfying Aggregation of Objectives by Duality".- "Interactive Algorithm for Multiobjective Optimization".- "Ranking of Multiattribute Alternatives with an Application to Coal Power Plant Siting".- "Efficient Stopping of a Random Series of Partially Ordered Points".- "An Interactive Branch and Bound Procedure for Multicriterion Integer Linear Programming".- "The Use of Reference Objectives in Multiobjective Optimization".- "Multiperiod Portfolio Selection and Capital Asset Pricing".- "BehaviorBases and Habitual Domains of Human Decision/ Behavior - Concepts and Applications".- "Methods for Solving Management Problems Involving Multiple Objectives".- Conference Program.- List of Participants.
01 Jan 1980
TL;DR: In this paper, the authors provide an introduction to the nature of MOLFP and the differences between a multiple objective linear fractional program (MOLFP) and a MOLP are identified in terms of the efficient sets they produce.
Abstract: This paper provides an introduction to the nature of multiple objective linear fractional programming. By graphically illustrating several examples, the differences between a multiple objective linear fractional program (MOLFP) and a MOLP are identified in terms of the efficient sets they produce. Instead of relying upon the usual notion of efficiency, a more relaxed definition of efficiency is used for computation. By exploiting its “near linearity”, a simplex-based algorithm for a MOLFP has been designed in [7]. It is similar to, but somewhat more elaborate than, those that have been devised for linear vector-maximum problems. The salient features of the MOLFP algorithm are reviewed in the light of the graphical examples that are provided.
01 Jan 1980
TL;DR: In this article, a dual of a given linear fractional program is defined and weak, direct and converse duality theorems are proved, and the equivalence of Charnes and Cooper dual and Dinkelbach's parametric dual is established.
Abstract: In this paper, a dual of a given linear fractional program is defined and the weak, direct and converse duality theorems are proved. Both the primal and the dual are linear fractional programs. This duality theory leads to necessary and sufficient conditions for the optimality of a given feasible solution. A unmerical example is presented to illustrate the theory in this connection. The equivalence of Charnes and Cooper dual and Dinkelbach’s parametric dual of a linear fractional program is also established.
TL;DR: In this paper, a duality theory for algebraic linear (integer) programming with linear algebraic objectives is developed, which is of the same importance for linear programming duality is for classical LP.
TL;DR: In this article, a method for enforcing additional constraints to linear fractional programs and showing its usefulness in solving integer LF programs is presented. But this method is not suitable for integer linear fractionals.
Abstract: This note consists of developing a method for enforcing additional constraints to linear fractional programs and showing its usefulness in solving integer linear fractional programs.
01 Jan 1980
TL;DR: Changes or probable errors in input data in a Multiple Objective Linear Program raise the following question: What are the limits within which parameters can be varied without affecting the solution?
Abstract: Changes or probable errors in input data in a Multiple Objective Linear Program raise the following question: What are the limits within which parameters can be varied without affecting the solution?
TL;DR: A compact algorithm for computing the stationary point of a quadranc function subject to hnear constraints is presented.
Abstract: REFERENCE 1. BETTS, J T A compact algorithm for computing the stationary point of a quadranc function subject to hnear constraints. ALGORITHM [ S u m m a r y i n f o r m a t i o n a n d p a r t of the listing are p r i n t e d here. T h e c o m p l e t e listing is available from t h e A C M A l g o r i t h m s D i s t r i b u t i o n Service (see inside b a c k cover for order form) or m a y be f o u n d in \"Collected A l g o r i t h m s from A C M. \" ] Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery To copy otherwise, or to republish, requires a fee and/or specific permission Author's address
01 Jan 1980
TL;DR: The results of the numerical comparative experiment with the simplex method are presented in this paper, and the method for solving the typical linear optimal control problem is grounded, while the adaptive method for linear programming problems is described.
Abstract: The results of the authors and their colleagues on investigation of linear programming problems and their application are given in the report. The adaptive method for solving the general linear programming problem is described. The results of the numerical comparative experiment with the simplex method are presented. New methods for solving the large linear programming problems are given. The method for solving the typical linear optimal control problem is grounded.
TL;DR: Khachian observes that Richard M. Karp has posed the question of whether (i) is a so-called "complete problem in the class NP" that is a large class of varied problems whose cost of solution appears inherently to grow exponentially with the size of the problem.
Abstract: problem, i . e . to maximize cTx f o r a g iven nvector C , with X subject to the constraints (i). A large class of other problems which are reducible to (i) can likewise be solved at polynomial cost. Khachian observes that Richard M. Karp [2] has posed the question of whether (i) is a so-called "complete problem in the class NP" that is a large class of varied problems whose cost of solution appears inherently to grow exponentially with the size of the problem. If it could be shown that the problem (1) is complete in NP , then all such problems (including many of great practical importancej could be solved at polynomial cost.
01 Jan 1980
TL;DR: In this paper, a nonnegative integral solution of a system of linear equations is given, if such a solution exists, using a combination of artificial basis technique and a method of integer forms.
Abstract: A method to obtain a nonnegative integral solution of a system of linear equations, if such a solution exists is given. The method writes linear equations as an integer programming problem and then solves the problem using a combination of artificial basis technique and a method of integer forms.
TL;DR: In this paper, the authors give a complete parametric solution to the problem of finding a claim size distribution F on the finite interval ω, maximizing the stop-loss premium corresponding to a given excess e, under the constraints that the first moment of F be at most equal to μ and the second equal to ν.
Abstract: We give a complete parametric solution of the following problem: Find a claim size distribution F on the finite interval [ο, ω], maximizing the stop-loss premium corresponding to a given excess e , under the constraints that the first moment of F be at most equal to μ and the second at most equal to ν The method used is the duality technique in semi-continuous linear programming described in De Vylder (1978) This technique is summarized, without proofs, in the first part of the paper.
TL;DR: An algorithm is presented which determines, given two Boolean functions, theSet of affine transformations and the set of general linear transformations under which the functions are equivalent.
Abstract: An algorithm is presented which determines, given two Boolean functions, the set of affine transformations and the set of general linear transformations under which the functions are equivalent. A method for detecting linear functions is developed for use in the algorithm.
01 Jan 1980
TL;DR: In this article, the duality theory for continuous linear programming problems is extended to problems defined in spaces of -p-times BocHNEB-integrable abstract functions (1 < p < ∞).
Abstract: In this paper the duality theory for continuous linear programming problems is extended to problems defined in spaces of -p-times BocHNEB-integrable abstract functions (1 < p < ∞). Two duality theorems are proved, the first one including the existence of a primal optimal solution, the second one the existence of a dual optimal solution. As introduction the paper contains a short survey on results obtained in the field of duality theory for continuous programs, too.