Optimization of first-order Nicoletti boundary value problem with discrete and differential inclusions and duality

Mahmudov E.

OPTIMIZATION, cilt.73, sa.3, ss.899-923, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 73 Sayı: 3
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1080/02331934.2022.2130698
  • Dergi Adı: OPTIMIZATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, Computer & Applied Sciences, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.899-923
  • Anahtar Kelimeler: Infimal convolution, duality, Nicoletti boundary value problem, Euler-Lagrange, polyhedral, EVOLUTION INCLUSIONS, MAYER PROBLEM
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

This paper is devoted to optimal control of the first-order Nicoletti boundary value problem (BVP) with discrete and differential inclusions (DFIs) and duality. First, we define Nicoletti-type problem with discrete inclusions, formulate optimality conditions for it and, based on the concept of infimal convolution, dual problems. Then, using the auxiliary discrete-approximate problem, we construct dual problems for Nicoletti DFIs and prove the duality theorems. Here, for the transition to the continuous problem, some results on the equivalence of locally adjoint mappings and support functions to the graph of set-valued mapping are proved. It turns out that the Euler-Lagrange type inclusions are 'duality relations' for both primal and dual problems, which means that a pair consisting of solutions to the primal and dual problems satisfies this extremal relation and vice versa. Finally, as an appication of the results obtained, we consider the first-order Nicoletti BVP with polyhedral DFIs.