Optimality Conditions of Approximate Solutions for Nonsmooth Semi-infinite Programming Problems  

作　　者：Xian-Jun Long Yi-Bin Xiao Nan-Jing Huang 

机构地区：[1]College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China [2]School of Mathematical Science,University of Electronic Science and Technology of China,Chengdu 611731,China [3]Department of Mathematics,Sichuan University,Chengdu 610064,China

出　　处：《Journal of the Operations Research Society of China》2018年第2期289-299,共11页中国运筹学会会刊（英文）

基　　金：This work was partially supported by the National Natural Science Foundation of China(Nos.11471059 and 11671282);the Chongqing Research Program of Basic Research and Frontier Technology(Nos.cstc2014jcyjA00037,cstc2015jcyjB00001 and cstc2014jcyjA00033);the Education Committee Project Research Foundation of Chongqing(Nos.KJ1400618 and KJ1400630);the Program for University Innovation Team of Chongqing(No.CXTDX201601026);the Education Committee Project Foundation of Bayu Scholar.

摘　　要：In this paper,we study optimality conditions of approximate solutions for nonsmooth semi-infinite programming problems.Three new classes of functions,namelyε-pseudoconvex functions of type I and type II andε-quasiconvex functions are introduced,respectively.By utilizing these new concepts,sufficient optimality conditions of approximate solutions for the nonsmooth semi-infinite programming problem are established.Some examples are also presented.The results obtained in this paper improve the corresponding results of Son et al.(J Optim Theory Appl 141:389–409,2009).

关 键 词：Nonsmooth semi-infinite programming problem Optimality condition Approximate solution Generalized pseudoconvexity 

分 类 号：O22[理学—运筹学与控制论]