非光滑向量均衡问题近似拟全局真有效解的最优性条件  

Optimality Conditions for Approximate Quasi Globally Proper Efficient Solutions to Nonsmooth Vector Equilibrium Problems

作　　者：韩文艳 余国林[1] HAN WENYAN;YU GUOLIN(Institute of A pplied Mathematics,North Minzu University,Yinchuan 750021,China)

机构地区：[1]北方民族大学应用数学数学研究所,银川750021

出　　处：《应用数学学报》2021年第1期49-60,共12页Acta Mathematicae Applicatae Sinica

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

摘　　要：本文研究一类非光滑向量均衡问题(Vector Equilibrium Problem)(VEP)关于近似拟全局真有效解的最优性条件.首先,利用凸集的拟相对内部型分离定理和Clarke次微分的性质,得到了问题(VEP)关于近似拟全局真有效解的最优性必要条件.其次,引入近似伪拟凸函数的概念,并给出具体实例验证其存在性,且在该凸性假设下建立了问题(VEP)关于近似拟全局真有效解的充分条件.最后,利用Tammer函数以及构建满足一定性质的非线性泛函,得到了问题(VEP)近似拟全局真有效解的标量化定理.This paper is devoted to investigate the optimality conditions for approximate quasi globally proper efficient solutions for a class of nonsmooth Vector Equilibrium Problem(VEP).Firstly,a necessary optimality condition to problem(VEP) for approximate quasi globally proper efficient solutions is established by utilizing the separation theorem with respect to the quasi relative interior of convex sets and the properties of the Clarke subdifferential.Secondly,the concept of approximate pseudoconvex function is introduced,and its existence is verified by a concrete example.Under the assumption of introduced convexity,a sufficient optimality condition for problem(VEP) in sense of approximate quasi globally proper efficiency is also presented.Finally,by using Tammer’s function and constructing the nonlinear functional with mild conditions,the scalarization theorems of the approximate quasi globally proper efficient solutions to the problem(VEP) are proposed.

关 键 词：向量均衡问题 真有效解 广义凸性 最优性条件 标量化 

分 类 号：O212.7[理学—概率论与数理统计]