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

被引：21
|
作者：
Long X.-J. [1 ]
Xiao Y.-B. [2 ]
Huang N.-J. [3 ]
机构：
[1] College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing
[2] School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu
[3] Department of Mathematics, Sichuan University, Chengdu
来源：
Journal of the Operations Research Society of China | 2018年 / 6卷 / 2期
基金：
中国国家自然科学基金;
关键词：
Approximate solution; Generalized pseudoconvexity; Nonsmooth semi-infinite programming problem; Optimality condition;
D O I：
10.1007/s40305-017-0167-1
中图分类号：
学科分类号：
摘要：
In this paper, we study optimality conditions of approximate solutions for nonsmooth semi-infinite programming problems. Three new classes of functions, namely ε-pseudoconvex functions of type I and type II and ε-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). © 2017, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag Berlin Heidelberg.
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页码：289 / 299
页数：10
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