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

Elimhan N. Mahmudov*, Sevilay Demir Saǧlam

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)407-424
Number of pages18
JournalGeorgian Mathematical Journal
Volume29
Issue number3
DOIs
Publication statusPublished - 1 Jun 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 Walter de Gruyter GmbH, Berlin/Boston.

Keywords

  • adjoint
  • approximation
  • differential inequality
  • Discrete inequality
  • inclusion

Fingerprint

Dive into the research topics of 'Necessary and sufficient conditions of optimality for second order discrete and differential inequalities'. Together they form a unique fingerprint.

Cite this