非凸集值优化问题E-Benson真有效元的最优性条件  

The Optimality Conditions of E-Benson Proper Efficient Element for Nonconvex Set-valued Optimization Problems

作　　者：吴唯钿 仇秋生[1] 田伟福[2] WU WEITIAN;Qiu QIUSHENG;TIAN WEIFU(Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China;Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China;Office of Budget and Finance,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]浙江师范大学数学系,金华321004 [2]浙江师范大学计划财务处,金华321004

出　　处：《应用数学学报》2018年第5期620-631,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11471291)资助项目

摘　　要：本文首先给出了集合为近似E-次类凸的等价刻画.其次,分别在锥具有紧基和弱紧基的条件下,获得了近似E-次类凸集值优化问题的E-Benson真有效元的Lagrange乘子定理.作为应用,获得了集值优化问题Benson真有效元的Lagrange乘子定理.最后,给出了集值优化问题E-鞍点的充分条件.In this paper, firstly, an equivalent characterization of a set is nearly E-subconvexlike is given. Then, Lagrange multiplier theorem of E-Benson proper efficient element of nearly E-subconvexlike set-valued optimization under the condition of cone with compact base or weak compact base is obtained. As application, Lagrange multiplier theorem of Benson proper efficient element of set-valued optimization problems is derived. At last, E-saddle points theorem for set-valued optimization problems is presented.

关 键 词：Benson真有效元 改进集 最优性条件 LAGRANGE乘子定理 

分 类 号：O221.6[理学—运筹学与控制论]