Topic
Fractional programming
About: Fractional programming is a research topic. Over the lifetime, 2973 publications have been published within this topic receiving 92588 citations.
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TL;DR: It is shown that solutions obtained by fuzzy linear programming are always efficient solutions and the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution are shown.
3,357 citations
Book•
01 Aug 1989
TL;DR: Mathematical Background Topics from Linear Algebra Single Objective Linear Programming Determining all Alternative Optima Comments about Objective Row Parametric Programming Utility Functions, Nondominated Criterion Vectors and Efficient Points Point Estimate Weighted-sums Approach.
Abstract: Mathematical Background Topics from Linear Algebra Single Objective Linear Programming Determining all Alternative Optima Comments about Objective Row Parametric Programming Utility Functions, Nondominated Criterion Vectors and Efficient Points Point Estimate Weighted-sums Approach Optimal Weighting Vectors, Scaling and Reduced Feasible Region Methods Vector-Maximum Algorithms Goal Programming Filtering and Set Discretization Multiple Objective Linear Fractional Programming Interactive Procedures Interactive Weighted Tchebycheff Procedure Tchebycheff/Weighted-Sums Implementation Applications Future Directions Index.
3,280 citations
2,617 citations
TL;DR: In this paper, an algorithm for fractional programming with nonlinear as well as linear terms in the numerator and denominator is presented. But the algorithm is based on a theorem by Jagannathan Jagannathy, R. 1966.
Abstract: The main purpose of this paper is to delineate an algorithm for fractional programming with nonlinear as well as linear terms in the numerator and denominator. The algorithm presented is based on a theorem by Jagannathan Jagannathan, R. 1966. On some properties of programming problems in parametric form pertaining to fractional programming. Management Sci.12 609--615. concerning the relationship between fractional and parametric programming. This theorem is restated and proved in a somewhat simpler way. Finally, it is shown how the given algorithm can be related to the method of Isbell and Marlow Isbell, J. R., W. H. Marlow. 1956. Attrition games. Naval Res. Logist. Quart.3 71--93. for linear fractional programming and to the quadratic parametric approach by Ritter Ritter, K. 1962. Ein Verfahren zur Losung parameterabhangiger, nichtlinearer Maximum-Probleme. Unternehmensforschung, Band 6, S. 149--166.. The Appendix contains a numerical example.
2,531 citations
Book•
01 Jan 1969
TL;DR: It is shown that if A is closed for all k → x x, k → y y, where ( k A ∈ ) k y x , then ( ) A ∉ y x .
Abstract: Part 1 (if): Assume that Z is closed. We must show that if A is closed for all k → x x , k → y y , where ( k A ∈ ) k y x , then ( ) A ∈ y x . By the definition of Z being closed, we know that all points arbitrarily close to Z are in Z. Let k → x x , k → y y , and ( k A ∈ ) k y x . Now, for any ε > 0, there exists an N such that for all k ≥ N we have || || k ε − < x x , || || k ε − < y y which implies that ( ) , x y is arbitrarily close to Z, so ( ) , x y ∈ Z and ( ) A ∈ y x . Thus, A is closed.
2,146 citations