ϵ-Efficient solutions in semi-infinite multiobjective optimization

In this paper we apply some tools of nonsmooth analysis and scalarization method due to Chankong–Haimes to find ϵ -efficient solutions of semi-infinite multiobjective optimization problems (MP). We establish ϵ -optimality conditions of Karush–Kuhn–Tucker (KKT) type under Farkas–Minkowski (FM) constraint qualification by using ϵ -subdifferential concept. In addition we propose mixed type dual problem (including dual problems of Wolfe and Mond–Weir types as special cases) for ϵ -efficient solutions and investigate relationship between mentioned (MP) and its dual problem as well as establish several ϵ -duality theorems.