Second-order viability problems for differential inclusions with endpoint constraint and duality. Issue 3 (11th February 2022)

• Record Type: Journal Article
• Authors: Mahmudov, Elimhan N.
• Is Part Of: Applicable analysis. Volume 101:Issue 3(2022)
• Page Start: 1130
• Page End: 1146
• Publication Date: 2022-02-11
• Subjects: Infimal convolution -- duality -- endpoint constraint -- Euler–Lagrange -- viability; 34A60 -- 49N15 -- 49M25 -- 90C46; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1773444
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: The paper deals with the optimal control of second-order viability problems for differential inclusions with endpoint constraint and duality. Based on the concept of infimal convolution and new approach to convex duality functions, we construct dual problems for discrete and differential inclusions and prove the duality results. It seems that the Euler–Lagrange type inclusions are 'duality relations' for both primary and dual problems. Finally, some special cases show the applicability of the general approach; duality in the control problem with second-order polyhedral DFIs and endpoint constraints defined by a polyhedral cone is considered.