- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 6
- On duality in convex optimization of second-order differential inclusions with periodic boundary con...
On duality in convex optimization of second-order differential inclusions with periodic boundary conditions
Authors : Sevilay Demir Sağlam, Elimhan Mahmudov
Pages : 1588-1599
Doi:10.15672/hujms.1056259
View : 11 | Download : 4
Publication Date : 2022-12-01
Article Type : Research
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