The Duality of Convex Optimization Problem for Differential Inclusions

DEMİR SAĞLAM S., Mahmudov E.

5th International Conference of Mathematical Sciences, ICMS 2021, İstanbul, Turkey, 23 - 27 June 2021, vol.2483 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 2483
  • Doi Number: 10.1063/5.0117079
  • City: İstanbul
  • Country: Turkey
  • Keywords: Boundary-value Problem, Duality, Locally adjoint mappings, Transversality
  • Istanbul Technical University Affiliated: Yes


© 2022 American Institute of Physics Inc.. All rights reserved.The purpose of this paper is to investigate the duality for optimal control problems with higher-order differential inclusions. Using locally adjoint mappings and the discretization method, we derive the conditions of optimality for a boundary-value problem with higher-order differential inclusions. This method connects a duality relation problem to a continuous concerning problem. Then, thanks to the dual operations of addition and infimal convolution of convex functions, we obtain duality results. In general, the construction of the duality problem with the assistance of discrete and discrete approximation problems necessitates a significant amount of effort to comprehend the computational aspects. Finally, we show that the optimal solutions to the primal convex and dual concave problems are the same.