Approximate Optimality Conditions for Composite Convex Optimization Problems  

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

机构地区：[1]College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China [2]College of Mathematics and Statistics,Chongqing JiaoTong University,Chongqing 400074,China

出　　处：《Journal of the Operations Research Society of China》2017年第4期469-485,共17页中国运筹学会会刊（英文）

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).

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 semicontinuous.By using the properties of the epigraph of conjugate functions,we introduce a new regularity condition and give its equivalent characterizations.Under this new regularity condition,we derive necessary and sufficient optimality conditions ofε-optimal solutions for the composite convex optimization problem.As applications of our results,we derive approximate optimality conditions to cone-convex optimization problems.Our results extend or cover many known results in the literature.

关 键 词：Composite convex optimization problem Approximate optimality condition Generalized regularity condition ε-Subdifferential 

分 类 号：O17[理学—数学]