On duality in convex optimization of second-order differential inclusions with periodic boundary conditions

Authors : Sevilay DEMİR SAĞLAM, Elimhan MAHMUDOV

Pages : 1588-1599

Doi:10.15672/hujms.1056259

View : 28 | Download : 13

Publication Date : 2022-12-01

Article Type : Research Paper

Abstract :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 formulating 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.
Keywords : differential inclusion, optimality conditions, duality, transversality condition