Optimality conditions and duality results for a new class of nonconvex nonsmooth vector optimization problems

[摘要] 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,ro)^{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,ro)^{w}-invexity are applicable for a larger class of nonconvex nondifferentiable multiobjective programming problems than under several generalized convexity notions existing in the literature.

[学科分类] 数学（综合）

[关键词] nonsmooth mutiobjective programming;efficient solution;nonsmooth (Φ;ρ) w -invexity;optimality conditions;Mond-Weir duality