New Second-order Contingent Epiderivatives and Set-valued Optimization Problems  

作　　者：Sheng-kun ZHU Sheng-jie LI 

机构地区：[1]College of Economic Mathematics,Southwestern University of Finance and Economics [2]College of Mathematics and Statistics,Chongqing University

出　　处：《Acta Mathematicae Applicatae Sinica》2016年第4期983-994,共12页应用数学学报（英文版）

基　　金：Supported in part by the National Natural Science Foundation of China under Grant No.11601437,11526165and 11571055;the Scientific Research Fund of Sichuan Provincial Science and Technology Department under Grant No.2015JY0237;the Fundamental Research Funds for the Central Universities under Grant No.JBK160129

摘　　要：In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investigate some special properties of the second-order compound contingent epiderivative. By virtue of the second-order compound contingent epiderivative, we establish some unified second-order sufficient and necessary optimality conditions for set-valued optimization problems. All results in this paper generalize the corresponding results in the literature.In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investigate some special properties of the second-order compound contingent epiderivative. By virtue of the second-order compound contingent epiderivative, we establish some unified second-order sufficient and necessary optimality conditions for set-valued optimization problems. All results in this paper generalize the corresponding results in the literature.

关 键 词：set-valued optimization second-order compound contingent epiderivative optimality conditions 

分 类 号：O224[理学—运筹学与控制论]