Duality theory for optimization problems with interval-valued objective functions
type: Item
instance of: scholarly article
title: Duality theory for optimization problems with interval-valued objective functions
zbMATH Open document ID: 1198.90365
author: Hsien-Chung Wu
published in: Journal of Optimization Theory and Applications
publication date: 2010-04-21T00:00:00Z
review text: To solve the investigated interval-valued nonlinear optimization problems a partial ordering of closed intervals is applied. Using this, a solution concept is suggested which is similar to the concept of a (weakly) nondominated solution in multicriterial optimization. To derive duality results, a Lagrange function is formulated which, for interval-valued optimization problems, is again interval-valued. Hence, the dual optimization problem is an interval-valued optimization problem, too. The weak duality result has then the form that, at feasible points, the dual objective function cannot dominate the primal one. Under convexity assumptions and if Slater's condition is satisfied it can be shown that there is no duality gap which means that the sets of optimal solutions of the primal and the dual problem intersect.
reviewed by: Stephan Dempe
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 5696841
zbMATH Keywords: interval-valued optimization
zbMATH Keywords: nonlinear optimization
zbMATH Keywords: weak duality
zbMATH Keywords: strong duality
MaRDI profile type: Publication
full work available at URL: s10957-009-9613-5
OpenAlex ID: W2146795783
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DOI: 10.1007/S10957-009-9613-5
description: scientific article; zbMATH DE number 5696841