Saddle points criteria in nondifferentiable multiobjective programming with VV-invex functions via an ηη-approximation method

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