一类Lipschitz B-(p,γ)-不变凸函数与非光滑规划

摘要

In this paper, we give a new class of Lipschitz B-(p, γ)-invex functions, which is generalizations of B-invex function and (p, γ)-invex function. Under this class of Lipschitz B-(p, γ)-invexity, we establish necessary and sufficient optimality conditions for nonsmooth programming problem. Furthermore, Mond-Weir type dual and Wolfe type dual are discussed, and theorems of weak duality, strong duality and strict converse duality are presented. The results obtained in this paper generalize the corresponding results on programming problems with convex function, B-invex function and (p, γ)-invex function.%设本文给出了一类新的Lipschitz B-(p,γ)-不变凸函数,它是B-不变凸函数和(p,γ)-不变凸函数的推广.在这类Lipschitz B-(p,γ)一不变凸性下,建立了非光滑规划的必要和充分最优性条件,讨论了Mond-Weir型对偶和Wolfe型对偶,证明了弱对偶、强对偶和逆对偶定理.所得结果推广了涉及凸函数、B-不变凸函数和(p,γ)-不变凸函数的规划问题的相应结果.