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Saddle point criteria and duality in multiobjective programming via an η-approximation method

Published online by Cambridge University Press:  17 February 2009

Tadeusz Antczak
Tadeusz Antczak
Affiliation:
Faculty of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland; e-mail: antczak@math.uni.lodz.pl.
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Abstract

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In this paper, Antczak's η-approximation approach is used to prove the equivalence between optima of multiobjective programming problems and the η-saddle points of the associated η-approximated vector optimisation problems. We introduce an η-Lagrange function for a constructed η-approximated vector optimisation problem and present some modified η-saddle point results. Furthermore, we construct an η-approximated Mond-Weir dual problem associated with the original dual problem of the considered multiobjective programming problem. Using duality theorems between η-approximation vector optimisation problems and their duals (that is, an η-approximated dual problem), various duality theorems are established for the original multiobjective programming problem and its original Mond-Weir dual problem.

Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 2 , October 2005 , pp. 155 - 172
Copyright
Copyright © Australian Mathematical Society 2005

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