Approximate Optimality Conditions for Composite Convex Optimization Problems

作     者：Xian-Jun Long Xiang-Kai Sun Zai-Yun Peng 

作者机构：College of Mathematics and StatisticsChongqing Technology and Business UniversityChongqing 400067China College of Mathematics and StatisticsChongqing JiaoTong UniversityChongqing 400074China 

出 版 物：《Journal of the Operations Research Society of China》 (中国运筹学会会刊（英文）)

年 卷 期：2017年第5卷第4期

页      面：469-485页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：the National Natural Science Foundation of China(Nos.11471059,11301571,and 11301570) the Chongqing Research Program of Basic Research and Frontier Technology(Nos.cstc2014jcyjA00037,cstc2015jcyjB00001,cstc2015jcyjA00025,and cstc2015jcyjA00002) the Education Committee Project Research Foundation of Chongqing(Nos.KJ1400618 and KJ1500626) the Postdoctoral Science Foundation of China(Nos.2015M580774 and 2016T90837) the Program for University Innovation Team of Chongqing(CXTDX201601026 and CXTDX201601022) 

主　　题：Composite convex optimization problem Approximate optimality condition Generalized regularity condition ε-Subdifferential 

摘      要：The purpose of this paper is to study the approximate optimality condition for composite convex optimization problems with a cone-convex system in locally convex spaces,where all functions involved are not necessarily lower semi*** using the properties of the epigraph of conjugate functions,we introduce a new regularity condition and give its equivalent *** this new regularity condition,we derive necessary and sufficient optimality conditions ofε-optimal solutions for the composite convex optimization *** applications of our results,we derive approximate optimality conditions to cone-convex optimization *** results extend or cover many known results in the literature.