OPTIMALITY CONDITIONS AND DUALITY RESULTS FOR A NEW CLASS OF NONCONVEX NONSMOOTH VECTOR OPTIMIZATION PROBLEMS

In this paper, a new class of nonconvex nonsmooth multiobjective programming problems with both inequality and equality constraints defined in a real Banach space is considered. Under the nondifferentiable vectorial (Phi, rho)(w)-invexity notion introduced in the paper, optimality conditions and duality results in Mond-Weir sense are established for the considered nonsmooth vector optimization problem. It turns out that the results developed here under (Phi, rho)(w)-invexity are applicable for a larger class of nonconvex nondifferentiable multiobjective programming problems than under several generalized convexity notions existing in the literature.