近似次微分刻画的约束向量均衡问题的最优性条件

数学物理学报 ›› 2022, Vol. 42 ›› Issue (2): 365-378.

近似次微分刻画的约束向量均衡问题的最优性条件

华盛信(),余国林*(),韩文艳(),孔翔宇()

北方民族大学数学与信息科学学院银川 750021

收稿日期:2021-05-19 出版日期:2022-04-26 发布日期:2022-04-18
通讯作者: 余国林 E-mail:1445143549@qq.com;guolin_yu@126.com;1965447108@qq.com;kxywz08@163.com
作者简介:华盛信, E-mail: 1445143549@qq.com|韩文艳, E-mail: 1965447108@qq.com|孔翔宇, E-mail: kxywz08@163.com
基金资助:
国家自然科学基金(11861002);宁夏自然科学基金(2020AAC03237);北方民族大学重大专项(ZDZX201804)

Characterization of Optimality to Constrained Vector Equilibrium Problems via Approximate Subdifferential

Shengxin Hua(),Guolin Yu*(),Wenyan Han(),Xiangyu Kong()

School of Mathematics and Information Science, North Minzu University, Yinchuan 750021

Received:2021-05-19 Online:2022-04-26 Published:2022-04-18
Contact: Guolin Yu E-mail:1445143549@qq.com;guolin_yu@126.com;1965447108@qq.com;kxywz08@163.com
Supported by:
the NSFC(11861002);the NSF of Ningxia(2020AAC03237);the Major Projects of Northern University for Nationalities(ZDZX201804)

摘要/Abstract

摘要：

该文研究一类约束向量均衡问题(CVEP) 近似拟弱有效解的最优性条件和对偶定理. 首先, 建立了问题(CVEP) 近似拟弱有效解关于近似次微分形式的最优性必要条件. 其次, 引入了一种广义凸性的概念, 称之为近似伪拟type-Ⅰ函数, 并在其假设下, 获得了问题(CVEP) 近似拟弱有效解的最优性充分条件. 最后, 引入了问题(CVEP) 的广义近似Mond-Weir对偶模型, 并建立其与原问题间关于近似拟弱有效解的对偶定理.

关键词: 向量均衡, 近似解, 广义凸性, 最优性条件, 对偶

Abstract:

In this paper, we study the optimality conditions and duality theorems for a class of Constrained Vector Equilibrium Problem (CVEP) with respect to approximate quasi weak efficient solutions. Firstly, a necessary optimality condition related to approximate subdifferential of approximation quasi weak efficient solution to problem (CVEP) is established. Secondly, a kind of generalized convexity, named pseudo quasi type-Ⅰ function, is introduced, and under its assumption, a sufficient optimality condition is also obtained. Finally, the generalized approximate Mond-Weir dual model of problem (CVEP) is presented, and the dual theorems between with the primal problem are established.

Key words: Vector Equilibrium, Approximate solution, Generalized convexity, Optimality conditions, Duality

中图分类号:

O221

华盛信,余国林,韩文艳,孔翔宇. 近似次微分刻画的约束向量均衡问题的最优性条件[J]. 数学物理学报, 2022, 42(2): 365-378.

Shengxin Hua,Guolin Yu,Wenyan Han,Xiangyu Kong. Characterization of Optimality to Constrained Vector Equilibrium Problems via Approximate Subdifferential[J]. Acta mathematica scientia,Series A, 2022, 42(2): 365-378.

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