THE LAGRANGE PROBLEM FOR DIFFERENTIAL INCLUSIONS WITH BOUNDARY VALUE CONDITIONS AND DUALITY


Saglam S. D. , Mahmudov E.

PACIFIC JOURNAL OF OPTIMIZATION, vol.17, no.2, pp.209-225, 2021 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 2
  • Publication Date: 2021
  • Title of Journal : PACIFIC JOURNAL OF OPTIMIZATION
  • Page Numbers: pp.209-225
  • Keywords: duality, Boundary value, polyhedral, Euler-Lagrange, transversality, DISCRETE, OPTIMIZATION

Abstract

The present article studies the duality of the Lagrange problem of optimal control theory with the boundary value constraints given by second-order polyhedral differential inclusions. Our primary aim is to establish results of duality for a boundary value problem with second-order differential inclusions. As a supplementary problem, we consider differential problems and formulate sufficient conditions of optimality, including particular transversality conditions incorporating the Euler-Lagrange type inclusions. After constructing the dual problem for second-order polyhedral differential inclusions, we prove that the adjoint Euler-Lagrange inclusion is simultaneously a dual relationship, which is satisfied by the pair of solutions of the primal and dual problems. Furthermore, solving numerical examples illustrates the application of these results.