Optimality Conditions and Duality in Nonsmooth Multiobjective Programs

We study nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions. Two types of Karush-Kuhn-Tucker optimality conditions with support functions are introduced. Sufficient optimality conditions are presented by using generalized convexity and certain r...

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Main Authors:	Do Sang Kim, Hyo Jung Lee
Format:	Article
Language:	English
Published:	SpringerOpen 2010-01-01
Series:	Journal of Inequalities and Applications
Online Access:	http://dx.doi.org/10.1155/2010/939537

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spelling	doaj-e32f1a7af9a74c70aaafffbd6f1f6bb92020-11-24T23:30:08ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2010-01-01201010.1155/2010/939537Optimality Conditions and Duality in Nonsmooth Multiobjective ProgramsDo Sang KimHyo Jung LeeWe study nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions. Two types of Karush-Kuhn-Tucker optimality conditions with support functions are introduced. Sufficient optimality conditions are presented by using generalized convexity and certain regularity conditions. We formulate Wolfe-type dual and Mond-Weir-type dual problems for our nonsmooth multiobjective problems and establish duality theorems for (weak) Pareto-optimal solutions under generalized convexity assumptions and regularity conditions. http://dx.doi.org/10.1155/2010/939537
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Do Sang Kim Hyo Jung Lee
spellingShingle	Do Sang Kim Hyo Jung Lee Optimality Conditions and Duality in Nonsmooth Multiobjective Programs Journal of Inequalities and Applications
author_facet	Do Sang Kim Hyo Jung Lee
author_sort	Do Sang Kim
title	Optimality Conditions and Duality in Nonsmooth Multiobjective Programs
title_short	Optimality Conditions and Duality in Nonsmooth Multiobjective Programs
title_full	Optimality Conditions and Duality in Nonsmooth Multiobjective Programs
title_fullStr	Optimality Conditions and Duality in Nonsmooth Multiobjective Programs
title_full_unstemmed	Optimality Conditions and Duality in Nonsmooth Multiobjective Programs
title_sort	optimality conditions and duality in nonsmooth multiobjective programs
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1025-5834 1029-242X
publishDate	2010-01-01
description	We study nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions. Two types of Karush-Kuhn-Tucker optimality conditions with support functions are introduced. Sufficient optimality conditions are presented by using generalized convexity and certain regularity conditions. We formulate Wolfe-type dual and Mond-Weir-type dual problems for our nonsmooth multiobjective problems and establish duality theorems for (weak) Pareto-optimal solutions under generalized convexity assumptions and regularity conditions.
url	http://dx.doi.org/10.1155/2010/939537
work_keys_str_mv	AT dosangkim optimalityconditionsanddualityinnonsmoothmultiobjectiveprograms AT hyojunglee optimalityconditionsanddualityinnonsmoothmultiobjectiveprograms
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Optimality Conditions and Duality in Nonsmooth Multiobjective Programs

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