AN η-APPROXIMATION METHOD FOR NONSMOOTH MULTIOBJECTIVE PROGRAMMING PROBLEMS

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 funct...

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Bibliographic Details
Published in:The ANZIAM journal Vol. 49; no. 3; pp. 309 - 323
Main Author: ANTCZAK, TADEUSZ
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.01.2008
Subjects:
(weak) Pareto optimal point
49J52
90C26
90C29
90C46
Approximation
Mathematical programming
Multiple objective analysis
nonsmooth multiobjective programming
Optimization
V-invex function with respect to η
η-approximated vector optimization problem
η-approximated vector optimization problem
90C46
49J52
nonsmooth multiobjective programming
90C29
90C26
V-invex function with respect to η
(weak) Pareto optimal point
ISSN:1446-1811, 1446-8735
Online Access:Get full text
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Summary: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.
Bibliography:ark:/67375/6GQ-V0T4PKMK-7
ArticleID:00009
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PII:S1446181108000096
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1446-1811
1446-8735
DOI:10.1017/S1446181108000096