ANZIAM  J.  47 (2005), 155-172
Saddle point criteria and duality in multiobjective programming via an $\eta$-approximation method

Tadeusz Antczak
  Faculty of Mathematics
  University of Lódz
  Banacha 22
  90-238 Lódz
  Poland
    antczak@math.uni.lodz.pl


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