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, cilt.51, sa.6, ss.1588-1599, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 6
  • Basım Tarihi: 2022
  • Doi Numarası: 10.15672/hujms.1056259
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.1588-1599
  • Anahtar Kelimeler: differential inclusion, optimality conditions, duality, transversality condition, DISCRETE, EXISTENCE, EQUATIONS
  • İstanbul Üniversitesi Adresli: Evet

Özet

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 formu-lating 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.