Duality for multiobjective variational control problems with \((\Phi, \rho)\)-invexity
type: Item
instance of: scholarly article
title: Duality for multiobjective variational control problems with \((\Phi, \rho)\)-invexity
zbMATH Open document ID: 1314.65080
author: Tadeusz Antczak
published in: Calcolo
publication date: 2015-03-23T00:00:00Z
review text: The author considers a variational (multiobjective) control problem. In order to formulate a strong duality theorem, he gives the Karush-Kuhn-Tucker necessary optimality conditions for the considered multiobjective variational control problem (MVPP). The concept of \((\Phi, \rho)\)-invexity is extended to multiobjective variational control problems. The concept of efficiency is used to formulate an MV control dual problem in the sense of Mond-Weir and in the sense of Wolfe for the considered MVPP. Under \((\Phi, \rho)\)-invexity assumptions imposed on the functions involved in the considered multiobjective variational control problem, weak, strong, converse and strict converse dual theorems in the sense of Mond-Weir and in the sense of Wolfe are proved between the new class of multiobjective variational control problems and their duals.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C46
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 49N15
zbMATH DE Number: 6418677
zbMATH Keywords: efficient solution
zbMATH Keywords: \({(\Phi
zbMATH Keywords: \rho)}\)-invexity
zbMATH Keywords: duality
zbMATH Keywords: necessary optimality conditions
zbMATH Keywords: weak, strong converse
zbMATH Keywords: functional inequality
zbMATH Keywords: convex
zbMATH Keywords: hypotheses
zbMATH Keywords: Kuhn-Tucker constraint
zbMATH Keywords: control problems
zbMATH Keywords: Karush-Kuhn-Tucker optimality conditions
zbMATH Keywords: multiobjective variational control problems
reviewed by: Jan Lovíšek
MaRDI profile type: Publication
full work available at URL: s10092-013-0092-6
OpenAlex ID: W1973452245
Wikidata QID: Q59399240
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DOI: 10.1007/S10092-013-0092-6
description: scientific article; zbMATH DE number 6418677