AN η-APPROXIMATION APPROACH IN NONLINEAR VECTOR OPTIMIZATION WITH UNIVEX FUNCTIONS

Abstract

In this paper, the so-called η-approximation approach is used to obtain the sufficient conditions for a nonlinear multiobjective programming problem with univex functions with respect to the same function η. In this method, an equivalent η-approximated vector optimization problem is constructed by a modification of both the objective and the constraint functions in the original multiobjective programming problem at the given feasible point. Moreover, to find the optimal solutions of the original multiobjective problem, it sufficies to solve its associated η-approximated vector optimization problem. Finally, the description of the η-approximation algorithm for solving a nonlinear multiobjective programming problem involving univex functions is presented.