Fractional programming with convex quadratic forms and functions

This article is concerned with two global optimization problems (P1) and (P2). Each of these problems is a fractional programming problem involving the maximization of a ratio of a convex function to a convex function, where at least one of the convex functions is a quadratic form. First, the articl...

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Bibliographic Details
Published in:European journal of operational research Vol. 173; no. 2; pp. 351 - 369
Main Author: Benson, Harold P.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.09.2006
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
Algorithms
Applied sciences
Branch & bound algorithms
Branch and bound
Exact sciences and technology
Fractional programming
Global optimization
Operational research. Management science
Operations research
Optimization algorithms
Problem solving
Quadratic form
Studies
Global optimization
Fractional programming
Branch and bound
Quadratic form
Branch and bound method
Global optimum
Convex function
Quadratic programming
Rational function
Convex programming
Quadratic function
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:This article is concerned with two global optimization problems (P1) and (P2). Each of these problems is a fractional programming problem involving the maximization of a ratio of a convex function to a convex function, where at least one of the convex functions is a quadratic form. First, the article presents and validates a number of theoretical properties of these problems. Included among these properties is the result that, under a mild assumption, any globally optimal solution for problem (P1) must belong to the boundary of its feasible region. Also among these properties is a result that shows that problem (P2) can be reformulated as a convex maximization problem. Second, the article presents for the first time an algorithm for globally solving problem (P2). The algorithm is a branch and bound algorithm in which the main computational effort involves solving a sequence of convex programming problems. Convergence properties of the algorithm are presented, and computational issues that arise in implementing the algorithm are discussed. Preliminary indications are that the algorithm can be expected to provide a practical approach for solving problem (P2), provided that the number of variables is not too large.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2005.02.069