Optimality and duality in nonsmooth multiobjective optimization involving generalized type I functions
type: Item
instance of: scholarly article
title: Optimality and duality in nonsmooth multiobjective optimization involving generalized type I functions
zbMATH Open document ID: 1140.90490
DOI: 10.1016/S0898-1221(03)00133-0
author: Tetsuzo Tanino
author: H. Kuk
publication date: 2004-08-06T00:00:00Z
review text: Convexity plays a very important role in optimization, in such a way that a number of generalizations of convexity have been proposed with the aim of obtain Karush-Kuhn-Tucker type suficient optimality conditions. In this work, the authors consider the following nonsmooth multiobjective (Pareto) optimization problem: \[ \min f(x),\; \text{ subject to } g(x)\leq 0 \tag{1} \] where \(f=(f_1,f_2, \cdots, f_p)\), \(g=(g_1,g_2, \cdots, g_m)\), \(f_i, g_j:X \rightarrow \mathbb{R}\), \(i=1,2,\dots ,p\), \(j=1,2,\dots ,m\), are locally Lipschitz functions on an open subset \(X\subset \mathbb{R}^n\) and min is considered in Pareto sense. The authors propose for the objective functions and the constraints a generalized invexity, called generalized Type I, expressed in terms of Clarke subdiferentials of the involved functions. Under these generalized Type I assumptions, using a Cottle constraint qualification, Karush-Kuhn-Tucker type necessary and sufficient conditions are given for a feasible point to be an efficient or properly efficient (in Geoffrion sense) solution for problem (1). Finally, Wolfe type and Mond-Weir type duals, under these generalized Type I assumptions, for problem (1) are analized.
reviewed by: V. Novo
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 2082276
zbMATH Keywords: nonsmooth multiobjective optimization
zbMATH Keywords: duality
zbMATH Keywords: invexity
zbMATH Keywords: type I functions
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2082276