G-α-预不变凸函数和非光滑向量优化  

G-α-preinvex functions and non-smooth vector optimization problems

作　　者：陈玉 颜学铃 邝凯 Chen Yu;Yan Xueling;Kuang Kai(School of Mathematics and Statistics,Guangxi Normal University,Guangxi 541004,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541004

出　　处：《纯粹数学与应用数学》2022年第2期236-245,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(11761014);广西省自然科学基金(2017GXNSFAA198243)。

摘　　要：通过推广α-不变凸函数和G-预不变凸函数,提出了一类非光滑G-α-预不变凸函数,在非光滑G-α-预不变凸条件下讨论非光滑向量优化问题的解与向量似变分不等式问题的解之间的关系,并证明了向量临界点,弱有效点与非光滑向量似变分不等式问题的解是等价的.In this paper, the non-smooth G-α-preinvex function is introduced by generalizing α-invex function and G-preinvex function, and some solution properties about non-smooth vector optimization problems and vector variational-like inequality problems are discussed under the condition of non-smooth G-α-preinvexity. Moreover, it is also proved that the vector critical points, weakly efficient points and the solutions of the nonsmooth weak vector variational-like inequality problem are equivalent under non-smooth pseudo-G-α-preinvexity assumptions.

关 键 词：向量似变分不等式问题 G-α-预不变凸函数 非光滑向量优化 弱有效点 

分 类 号：O221[理学—运筹学与控制论]