带约束集值向量均衡问题的鞍点存在条件  

Conditions for the Existence of Saddle Points in a Set-Valued Vector Equilibrium Problem with Constraints

作　　者：杨琪 张征[1] YANG Qi;ZHANG Zheng(School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2020年第2期152-158,共7页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11871059);四川省高校创新团队(16TD0019);西华师范大学英才基金(17YC379);西华师范大学校级教学改革与研究项目(jgxmyb18120)。

摘　　要：考虑了Hausdorff局部凸拓扑向量空间中带约束集值向量均衡问题的鞍点的存在性条件。首先,在Lagrange乘子属于有序集的极锥的拟内部情形下,建立了鞍点存在的充分性和必要性条件。此外,在Slater型约束条件下,得到了鞍点存在的重要结论,并利用该结论引进了弱有效解的概念。最后,在广义次似凸或预似凸的假设下,给出了带约束集值向量均衡问题的弱有效解的必要性条件。This paper talks about conditions for the existence of saddle points in a set-valued vector equilibrium problem with constraints in a Hausdorff locally convex topological vector space.First,sufficient and necessary conditions for the existence of saddle points are established in the case that Lagrange multiplier belongs to quasi-interior of the polar cone of the ordering set.Moreover,the existence of saddle points is obtained under the condition of Slater-type constraints qualifications and the concept of weak effective solution is introduced as well.Finally,the necessary conditions for weakly efficient solutions of set-valued vector equilibrium problems with constraints are given under the assumption of generalized subconvexlike or preconvexlike.

关 键 词：向量均衡问题 鞍点 Slater型约束条件 弱有效解 

分 类 号：O221[理学—运筹学与控制论]