On duality in convex optimization of second-order differential inclusions with periodic boundary conditions

Sevilay Demir Sağlam*, Elimhan N. Mahmudov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The present paper is devoted to the duality theory for the convex optimal control problem of second-order differential inclusions with periodic boundary conditions. First, we use an auxiliary problem with second-order discrete-approximate inclusions and focus on formulating sufficient conditions of optimality for the differential problem. Then, we concentrate on the duality that exists in periodic boundary conditions to establish a dual problem for the differential problem and prove that Euler-Lagrange inclusions are duality relations for both primal and dual problems. Finally, we consider an example of the duality for the second-order linear optimal control problem.

Original languageEnglish
Pages (from-to)1588-1599
Number of pages12
JournalHacettepe Journal of Mathematics and Statistics
Volume51
Issue number6
DOIs
Publication statusPublished - 2022

Bibliographical note

Publisher Copyright:
© 2022, Hacettepe University. All rights reserved.

Keywords

  • differential inclusion
  • duality
  • optimality conditions
  • transversality condition

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