Optimisation of parabolic type polyhedral discrete, discrete-approximate and differential inclusions

Mahmudov E., Mastaliyeva D.

International Journal of Control, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Doi Number: 10.1080/00207179.2023.2251614
  • Journal Name: International Journal of Control
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, zbMATH
  • Keywords: Approximate, discrete, necessary and sufficient, parabolic differential inclusions, polyhedral
  • Istanbul Technical University Affiliated: Yes

Abstract

The present paper is devoted to the optimisation of parabolic type differential inclusions (DFIs) given by polyhedral set-valued mappings. For this, an auxiliary problem with a polyhedral parabolic discrete inclusion is defined. With the help of locally adjoint mappings and comparison of matrix-coefficients of discrete and discrete-approximate problems, necessary and sufficient optimality conditions for polyhedral-parabolic discrete-approximate inclusions are skilfully constructed. Thus, using the discretisation method and the features of the polyhedral nature of the problem, we prove sufficient optimality conditions for a polyhedral parabolic DFI. At the end of the paper, the numerical results are presented.