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

Year 2022, Volume: 51 Issue: 6, 1588 - 1599, 01.12.2022

Sevilay Demir Sağlam , Elimhan Mahmudov

https://doi.org/10.15672/hujms.1056259

Cited By: 2

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

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