近似次微分刻画的约束向量均衡问题的最优性条件  

Characterization of Optimality to Constrained Vector Equilibrium Problems via Approximate Subdifferential

作　　者：华盛信 余国林 韩文艳 孔翔宇 Hua Shengxin;Yu Guolin;Han Wenyan;Kong Xiangyu(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021)

机构地区：[1]北方民族大学数学与信息科学学院,银川750021

出　　处：《数学物理学报（A辑）》2022年第2期365-378,共14页Acta Mathematica Scientia

基　　金：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(ZDZX-201804)。

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.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.

关 键 词：向量均衡 近似解 广义凸性 最优性条件 对偶 

分 类 号：O221[理学—运筹学与控制论]