OPTIMALITY AND DUALITY FOR GENERALIZED APPROXIMATE SOLUTIONS IN SEMI-INFINITE MULTIOBJECTIVE OPTIMIZATION

This paper is dedicated to a generalized ( α,e )-quasi-efficient solution to semi-infinite multiobjective optimization problems (SMP). Relationships between the mentioned solution of (SMP) and the corresponding solution of the scalar problem due to Chankong–Haimes are established. Using this equivalence, e -optimality conditions of Karush–Kuhn–Tucker (KKT) type are derived under the Farkas–Minkowski constraint qualification. In addition, we formulate dual problems of Wolfe and Mond–Weir types for (SMP), and prove weak and strong duality theorems.