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Duality Problems with Second-Order Polyhedral Discrete and Differential Inclusions

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Abstract

The present paper deals with the theory of duality for the Mayer problem given by second-order polyhedral discrete and differential inclusions. First, we formulate the conditions of optimality in the form of Euler–Lagrange type inclusions and transversality conditions for the polyhedral problems with second-order discrete and differential inclusions. Second, we establish dual problems for discrete and differential inclusions based on the infimal convolution concept of convex functions and prove the results of duality. For both primary and dual problems, the Euler–Lagrange type inclusions are “duality relations” and that the dual problem for discrete-approximate problems bridges the gap between the dual problems of discrete and continuous problems. As a result, the passage to the limit in the dual problem with discrete approximations plays a substantial role in the following investigations, without any which can hardly ever be established by any duality to the continuous problem. Furthermore, the numerical results also are provided.

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  • 16 April 2021

    The original article has been corrected due to incorrect affiliation.

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Acknowledgements

The authors wish to express their sincere thanks to the anonymous Editor of the Journal of Bulletin of the Iranian Mathematical Society and reviewers for valuable suggestions which improved the final manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Istanbul University, Istanbul, Turkey

    Sevilay Demir Sağlam

  2. Department of Mathematics, Istanbul Technical University, Istanbul, Turkey

    Elimhan Nadir Mahmudov

  3. Azerbaijan National Academy of Sciences, Institute of Control Systems, Baku, Azerbaijan

    Elimhan Nadir Mahmudov

Authors
  1. Sevilay Demir Sağlam
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  2. Elimhan Nadir Mahmudov
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Correspondence to Sevilay Demir Sağlam.

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Communicated by Xinmin Yang.

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Sağlam, S.D., Mahmudov, E.N. Duality Problems with Second-Order Polyhedral Discrete and Differential Inclusions. Bull. Iran. Math. Soc. 48, 537–562 (2022). https://doi.org/10.1007/s41980-021-00531-9

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