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

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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 \(\varepsilon \)-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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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Xian-Jun Long

  2. School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Yi-Bin Xiao

  3. Department of Mathematics, Sichuan University, Chengdu, 610064, China

    Nan-Jing Huang

Authors
  1. Xian-Jun Long
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  2. Yi-Bin Xiao
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  3. Nan-Jing Huang
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Corresponding author

Correspondence to Xian-Jun Long.

Additional information

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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Long, XJ., Xiao, YB. & Huang, NJ. Optimality Conditions of Approximate Solutions for Nonsmooth Semi-infinite Programming Problems. J. Oper. Res. Soc. China 6, 289–299 (2018). https://doi.org/10.1007/s40305-017-0167-1

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  • DOI: https://doi.org/10.1007/s40305-017-0167-1

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