向量变分不等式和多目标优化高阶严格极小解的关系  

Relationships between Vector Variational Inequality and Multi-objective Optimization for Strict Minimizer of Higher Order

作　　者：张亚萌 余国林[1] ZHANG Ya-meng;YU Guo-lin(Institute of Applied Mathematics,North Minzu University,Yinchuan 750021)

机构地区：[1]北方民族大学应用数学研究所,银川750021

出　　处：《工程数学学报》2021年第3期441-450,共10页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11861002);北方民族大学重大专项(ZDZX201804).

摘　　要：本文研究向量变分不等式与非光滑多目标优化问题高阶严格极小解之间的关系.首先,引入了一类广义高阶强伪凸Lipschitz函数的概念,称之为高阶强伪凸type I函数,并且给出具体实例说明其存在性.其次,在高阶强伪凸type I函数假设下,给出了高阶严格极小元,向量关键点和弱向量变分不等式解之间的关系刻画.This paper is devoted to the study of the relations between vector variational inequality and nonsmooth multi-objective optimization in the sense of strict minimizers of higher order.We firstly introduce an extension of higher-order strong pseudoconvexity for Lipschitz functions,termed higher-order strongly pseudoconvex functions of type I,and some examples are presented in the support of this generalization.Then,we identify the strict minimizers of higher order,the vector critical points and the solutions of the weak vector variational inequality problem under the higher-order strong pseudoconvexity of type I hypothesis.It is our understanding that such results have not been established till now.

关 键 词：多目标优化 高阶严格极小解 向量变分不等式 强凸性 

分 类 号：O212.7[理学—概率论与数理统计]