Formulas for Calculating Generalized Differentials with Respect to a Set and Their Applications

Thinh V. D., Qin X., Yao J.

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2024
  • Doi Number: 10.1007/s10957-024-02546-8
  • Journal Name: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

This paper provides formulas for calculating Fr & eacute;chet and limiting normal cones with respect to a set of sets and the limiting coderivative with respect to a set of set-valued mappings. These calculations are obtained under some qualification constraints and are expressed in the similar forms of the ones of Fr & eacute;chet and limiting normal cones and the limiting coderivative. By using these new formulas, we state explicit necessary optimality conditions with respect to a set for optimization problems with equilibrium constraints under certain qualification conditions. Some examples are also presented.