ANZIAM J.
47 (2005), 155172

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


Abstract

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

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