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


DEMİR SAĞLAM S., Mahmudov E.

Hacettepe Journal of Mathematics and Statistics, vol.51, no.6, pp.1588-1599, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 6
  • Publication Date: 2022
  • Doi Number: 10.15672/hujms.1056259
  • Journal Name: Hacettepe Journal of Mathematics and Statistics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.1588-1599
  • Keywords: differential inclusion, duality, optimality conditions, transversality condition
  • Istanbul University Affiliated: Yes

Abstract

© 2022, Hacettepe University. All rights reserved.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.