Necessary and sufficient conditions of optimality for second order discrete and differential inequalities

Mahmudov E., Saglam S. D.

GEORGIAN MATHEMATICAL JOURNAL, vol.29, pp.407-424, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29
  • Publication Date: 2022
  • Doi Number: 10.1515/gmj-2021-2134
  • Journal Name: GEORGIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.407-424
  • Keywords: Discrete inequality, differential inequality, inclusion, adjoint, approximation, OPTIMIZATION, INCLUSIONS
  • Istanbul Technical University Affiliated: Yes

Abstract

The present paper studies the optimization of the Bolza problem with a system of convex and nonconvex, discrete and differential state variable second-order inequality constraints by deriving necessary and sufficient conditions of optimality. The problem with a system of discrete-approximation inequalities is investigated using the proposed method of discretization and equivalence theorems for subdifferential inclusions, which greatly contributes to the derivation of adjoint discrete inclusions generated by a given system of nonlinear inequality constraints. Furthermore, we formulate sufficient conditions of optimality for the continuous problem by passing to the case of limit. A numerical example is provided to illustrate the theoretical approach's effectiveness.