Global optimization for a class of fractional programming problems
type: Item
instance of: scholarly article
title: Global optimization for a class of fractional programming problems
zbMATH Open document ID: 1206.90189
author: Shu-Cherng Fang
author: Ruey-Lin Sheu
author: David Y. Gao
author: Wenxun Xing
published in: Journal of Global Optimization
publication date: 2009-11-16T00:00:00Z
review text: The authors present a canonical dual approach to minimizing the sum of a quadratic function and the ratio of two quadratic functions subject to an elliptic constraint. First, they parameterize the original problem into a family of subprograms, in which each subproblem is a (possibly non-convex) quadratic program subject to one quadratic constraint. Then, it is shown that the infimum of the optima of the parameterized subproblems provides a solution to the original problem. For each subproblem a canonical dual subproblem is derived. For these pairs the authors provide some sufficient conditions to establish both the weak and strong duality theorems. The paper develops some existence conditions under which a global optimizer of the original problem can be identified by solving the corresponding canonical dual problems. Some numerical results using the quasi-Newton and line search methods are presented.
Mathematics Subject Classification ID: 90C32
Mathematics Subject Classification ID: 90C20
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 5633313
zbMATH Keywords: quadratic fractional programming
zbMATH Keywords: sum-of-ratios
zbMATH Keywords: global optimization
zbMATH Keywords: canonical duality
reviewed by: Francisco Guerra Vazquez
MaRDI profile type: Publication
full work available at URL: s10898-008-9378-7
OpenAlex ID: W1996396941
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DOI: 10.1007/S10898-008-9378-7
description: scientific article; zbMATH DE number 5633313