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AN η-APPROXIMATION METHOD FOR NONSMOOTH MULTIOBJECTIVE PROGRAMMING PROBLEMS

Part of: Existence theories

Published online by Cambridge University Press:  01 January 2008

TADEUSZ ANTCZAK
TADEUSZ ANTCZAK*
Affiliation:
Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland (email: antczak@math.uni.lodz.pl)
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Abstract

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In this paper, a new approach to a characterization of solvability of a nonlinear nonsmooth multiobjective programming problem with inequality constraints is introduced. A family of η-approximated vector optimization problems is constructed by a modification of the objective and the constraint functions in the original nonsmooth multiobjective programming problem. The connection between (weak) efficient points in the original nonsmooth multiobjective programming problem and its equivalent η-approximated vector optimization problems is established under V-invexity. It turns out that, in most cases, solvability of a nonlinear nonsmooth multiobjective programming problem can be characterized by solvability of differentiable vector optimization problems.

Keywords

nonsmooth multiobjective programmingV-invex function with respect to ηη-approximated vector optimization problem(weak) Pareto optimal point

MSC classification

Secondary: 90C26: Nonconvex programming, global optimization 90C29: Multi-objective and goal programming 90C46: Optimality conditions, duality 49J52: Nonsmooth analysis
Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 3 , January 2008 , pp. 309 - 323
Copyright
Copyright © Australian Mathematical Society 2008

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