Duality in the problems of optimal control described by Darboux-type differential inclusions


DEMİR SAĞLAM S.

OPTIMIZATION LETTERS, cilt.18, sa.8, ss.1811-1835, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 8
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s11590-023-02088-4
  • Dergi Adı: OPTIMIZATION LETTERS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1811-1835
  • Anahtar Kelimeler: Darboux differential inclusion, Duality, Optimality conditions
  • İstanbul Üniversitesi Adresli: Evet

Özet

This paper is devoted to the optimization of the Mayer problem with hyperbolic differential inclusions of the Darboux type and duality. We use the discrete approximation method to get sufficient conditions of optimality for the convex problem given by Darboux differential inclusions and the polyhedral problem for a hyperbolic differential inclusion with state constraint. We formulate the adjoint inclusions in the Euler-Lagrange inclusion and Hamiltonian forms. Then, we construct the dual problem to optimal control problem given by Darboux differential inclusions with state constraint and prove so-called duality results. Moreover, we show that each pair of primal and dual problem solutions satisfy duality relations and that the optimal values in the primal convex and dual concave problems are equal. Finally, we establish the dual problem to the polyhedral Darboux problem and provide an example to demonstrate the main constructions of our approach.