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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 3
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Research Article

Second-order viability problems for differential inclusions with endpoint constraint and duality

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Pages 1130-1146 | Received 12 Mar 2020, Accepted 19 May 2020, Published online: 05 Jun 2020
 

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.

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Acknowledgments

The author would like to express sincere thanks to the Editor-in-Chief Prof. Yongzhi Xu of the Journal of Applicable Analysis and anonymous reviewers for valuable suggestions that improved the final manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

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