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

Saglam S. D., Mahmudov E.

PACIFIC JOURNAL OF OPTIMIZATION, cilt.17, sa.2, ss.209-225, 2021 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 2
  • Basım Tarihi: 2021
  • Dergi Adı: PACIFIC JOURNAL OF OPTIMIZATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), MathSciNet, zbMATH
  • Sayfa Sayıları: ss.209-225
  • Anahtar Kelimeler: duality, Boundary value, polyhedral, Euler-Lagrange, transversality, DISCRETE, OPTIMIZATION
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

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.