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

Journal of the Operations Research Society of China - Tập 6 Số 2 - Trang 289-299 - 2018
Long, Xian-Jun1, Xiao, Yi-Bin2, Huang, Nan-Jing3
1College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, China
2School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu, China
3Department of Mathematics, Sichuan University, Chengdu, China

Tóm tắt

In this paper, we study optimality conditions of approximate solutions for nonsmooth semi-infinite programming problems. Three new classes of functions, namely $$\varepsilon $$ -pseudoconvex functions of type I and type II and $$\varepsilon $$ -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).

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Journal of the Operations Research Society of China

Tập 6 Số 2

289-299

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