Robust duality for fractional programming problems with constraint-wise data uncertainty
type: Item
instance of: scholarly article
title: Robust duality for fractional programming problems with constraint-wise data uncertainty
zbMATH Open document ID: 1242.90252
published in: Journal of Optimization Theory and Applications
publication date: 2012-01-12T00:00:00Z
review text: This paper deals with duality theory for examining and solving convex-concave fractional programming in the face of data uncertainty. The authors prove strong duality between the robust counterpart of an uncertain convex-concave fractional program and the optimistic counterpart of its conventional Wolfe dual program with uncertain parameters. For linear fractional programming problems with constraint-wise interval uncertainty, it is shown that the dual of the robust counterpart is indeed equivalent to the optimistic counterpart. Consequently, the authors also establish that a robust (worst-case) solution of a linear fractional programming problem with constraint-wise interval uncertainty can be found by solving a simple linear programming problem. It would be of interest to investigate whether strong duality can be used to find robust solutions of linear fractional problems easily with broad classes of uncertainty sets including the ellipsoidal uncertainty set that is often employed in robust optimization.
reviewed by: Samir Kumar Neogy
Mathematics Subject Classification ID: 90C32
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 5996883
zbMATH Keywords: Fractional programming under uncertainty
zbMATH Keywords: Strong duality
zbMATH Keywords: Robust optimization
zbMATH Keywords: Linear fractional programming with uncertainty
author: V. Jeyakumar
author: G. Li
MaRDI profile type: Publication
full work available at URL: s10957-011-9896-1
OpenAlex ID: W1998073116
Wikidata QID: Q59241543
cites work: Using duality to solve generalized fractional programming problems
cites work: Optimality conditions and duality for a class of nonlinear fractional programming problems.
cites work: A sixth bibliography of fractional programming
cites work: Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity
cites work: Q3182207
cites work: Robust optimization-methodology and applications
cites work: Selected topics in robust convex optimization
cites work: Extending scope of robust optimization: comprehensive robust counterparts of uncertain problems
cites work: Robust linear optimization under general norms.
cites work: Duality in robust optimization: Primal worst equals dual best
cites work: Strong Duality in Robust Convex Programming: Complete Characterizations
cites work: Q4821526
cites work: Convex Analysis
cites work: Fractional programming : a recent survey
cites work: Parameter-free convex equivalent and dual programs of fractional programming problems
cites work: Characterizing robust set containments and solutions of uncertain linear programs without qualifications
cites work: A robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty
cites work: Robust conjugate duality for convex optimization under uncertainty with application to data classification
DOI: 10.1007/S10957-011-9896-1
DBLP publication ID: journals/jota/JeyakumarL11
description: scientific article; zbMATH DE number 5996883