Multiobjective Programming under Nondierentiable G-V-Invexity

Abstract

In the paper, new Fritz John type necessary optimality conditions and new Karush-Kuhn-Tucker type necessary opimality conditions are established for the considered nondifferentiable multiobjective programming problem involving locally Lipschitz functions. The proof of them avoids the alternative theorem usually applied in such a case. The sufficiency of the introduced necessary optimality conditions are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem are G-V-invex with respect to the same function eta. Further, the so-called nondifferentiable vector G-Mond-Weir dual problem is defined for the considered nonsmooth multiobjective programming problem. Under nondifferentiable G-V-invexity hypotheses, various duality results are establsihed under the primal vector optimization problem
and its $G$-Mond-Weir dual problem.