Saddle points criteria in nondifferentiable multiobjective programming with V-invex functions via an η-approximation method

Abstract

The η-approximation method is used to a characterization of solvability of nonconvex nondifferentiable multiobjective programming problems. A family of η-approximated vector optimization problems is constructed in this approach for the original nondifferentiable multiobjective programming problem. The definitions of a vector-valued η-Lagrange function and of an η-saddle point for this family of η-approximated vector optimization problems are introduced. Thus, the equivalence between a (weak) Pareto optimum of the original multiobjective programming problems and an η-saddle point of the η-Lagrange function in its associated η-approximated vector optimization problems is established under V-invexity.