Saddle Point Criteria and Duality in Multiobjective Programming via an Η-approximation Method

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 Mond-Weir 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 Mond-Weir dual problem.