Journal of the Operations Research Society of China ›› 2018, Vol. 6 ›› Issue (2): 289-299.doi: 10.1007/s40305-017-0167-1

Special Issue: Non-smooth optimization

• Continuous Optimization • Previous Articles     Next Articles

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

Xian-Jun Long1 · Yi-Bin Xiao2 · Nan-Jing Huang3   

  1. 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
  • Online:2018-06-30 Published:2018-06-30
  • Supported by:

    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) and the Education Committee Project
    Foundation of Bayu Scholar.

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Abstract:

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

Key words: Nonsmooth semi-infinite programming problem ·, Optimality condition ·Approximate solution ·, Generalized pseudoconvexity

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