Gateaux可微条件下E-凸规划问题的解集刻画  

CHARACTERIZATION OF THE SOLUTION SET OF E-CONVEX PROGRAMMING WITH GATEAUX DIFFERENTIAL

作　　者：李均 彭建文 刘学文 LI Jun;PENG Jian-wen;LIU Xue-wen(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《数学杂志》2018年第6期1097-1106,共10页Journal of Mathematics

基　　金：重庆市基础科学与前沿技术研究重点项目基金资助(cstc2015jcyjBX0029);最优化与控制省部共建教育部重点实验室;重庆市高等学校巴渝学者特聘教授项目资助

摘　　要：本文研究了E-凸函数在Gateaux可微条件下Gateaux导数与E-次微分之间的关系,获得了E-凸规划问题最优解的必要条件.给出了E-凸规划问题的最优解集刻画.In this paper,we study the relation between the Gateaux differential of E-convex function and the E-differential,and obtain the necessary condition for the optimal solution of E-convex programming problems.According to these two conclusions,the optimal solution set characterization of E-convex programming problem is shown.

关 键 词：E-凸函数 E-凸规划 GATEAUX可微 解集刻画 

分 类 号：O221.2[理学—运筹学与控制论]