Optimization of the Hyperbolic Type Differential Inclusions Described by Polyhedral Set Valued Mappings

Gulseren Cicek; Elimhan N. Mahmudov

doi:10.1109/PCI60110.2023.10326021

Optimization of the Hyperbolic Type Differential Inclusions Described by Polyhedral Set Valued Mappings

Gulseren Cicek^*
, Elimhan N. Mahmudov

^*Corresponding author for this work

Department of Mathematics Engineering

Istanbul University
Institute of Control Systems Ministry of Science and Education Republic of Azerbaijan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper, sufficient conditions for the optimal problem regarding polyhedral hyperbolic differentials are obtained. Necessary and sufficient conditions for the polyhedral hyperbolic discrete problem are derived using the polyhedral nature of the problem. By the discretization method of hyperbolic DFIs, the optimality conditions for the polyhedral discrete approximate problem are formulated in the form of the Mahmudov adjoint inclusions. We establish sufficient optimality conditions for the polyhedral DFIs of hyperbolic type. To the best of our knowledge, these results are new in the literature and use the discretization method when creating the optimality conditions for polyhedral hyperbolic DFIs. This method differs from formerly used methods because of its polyhedral structure.

Original language	English
Title of host publication	2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9798350319064
DOIs	https://doi.org/10.1109/PCI60110.2023.10326021
Publication status	Published - 2023
Event	5th International Conference on Problems of Cybernetics and Informatics, PCI 2023 - Baku, Azerbaijan Duration: 28 Aug 2023 → 30 Aug 2023

Publication series

Name	2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023

Conference

Conference	5th International Conference on Problems of Cybernetics and Informatics, PCI 2023
Country/Territory	Azerbaijan
City	Baku
Period	28/08/23 → 30/08/23

Bibliographical note

Publisher Copyright:
© 2023 IEEE.

Keywords

Laplace operator
discrete-approximation
hyperbolic differential inclusions
optimality conditions
plyhedral

Access to Document

10.1109/PCI60110.2023.10326021

Cite this

Cicek, G., & Mahmudov, E. N. (2023). Optimization of the Hyperbolic Type Differential Inclusions Described by Polyhedral Set Valued Mappings. In 2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023 (2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/PCI60110.2023.10326021

Cicek, Gulseren ; Mahmudov, Elimhan N. / Optimization of the Hyperbolic Type Differential Inclusions Described by Polyhedral Set Valued Mappings. 2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023. Institute of Electrical and Electronics Engineers Inc., 2023. (2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023).

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title = "Optimization of the Hyperbolic Type Differential Inclusions Described by Polyhedral Set Valued Mappings",

abstract = "In this paper, sufficient conditions for the optimal problem regarding polyhedral hyperbolic differentials are obtained. Necessary and sufficient conditions for the polyhedral hyperbolic discrete problem are derived using the polyhedral nature of the problem. By the discretization method of hyperbolic DFIs, the optimality conditions for the polyhedral discrete approximate problem are formulated in the form of the Mahmudov adjoint inclusions. We establish sufficient optimality conditions for the polyhedral DFIs of hyperbolic type. To the best of our knowledge, these results are new in the literature and use the discretization method when creating the optimality conditions for polyhedral hyperbolic DFIs. This method differs from formerly used methods because of its polyhedral structure.",

keywords = "Laplace operator, discrete-approximation, hyperbolic differential inclusions, optimality conditions, plyhedral",

author = "Gulseren Cicek and Mahmudov, \{Elimhan N.\}",

note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023 ; Conference date: 28-08-2023 Through 30-08-2023",

year = "2023",

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language = "English",

series = "2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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Cicek, G & Mahmudov, EN 2023, Optimization of the Hyperbolic Type Differential Inclusions Described by Polyhedral Set Valued Mappings. in 2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023. 2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023, Institute of Electrical and Electronics Engineers Inc., 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023, Baku, Azerbaijan, 28/08/23. https://doi.org/10.1109/PCI60110.2023.10326021

Optimization of the Hyperbolic Type Differential Inclusions Described by Polyhedral Set Valued Mappings. / Cicek, Gulseren; Mahmudov, Elimhan N.
2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023. Institute of Electrical and Electronics Engineers Inc., 2023. (2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - In this paper, sufficient conditions for the optimal problem regarding polyhedral hyperbolic differentials are obtained. Necessary and sufficient conditions for the polyhedral hyperbolic discrete problem are derived using the polyhedral nature of the problem. By the discretization method of hyperbolic DFIs, the optimality conditions for the polyhedral discrete approximate problem are formulated in the form of the Mahmudov adjoint inclusions. We establish sufficient optimality conditions for the polyhedral DFIs of hyperbolic type. To the best of our knowledge, these results are new in the literature and use the discretization method when creating the optimality conditions for polyhedral hyperbolic DFIs. This method differs from formerly used methods because of its polyhedral structure.

AB - In this paper, sufficient conditions for the optimal problem regarding polyhedral hyperbolic differentials are obtained. Necessary and sufficient conditions for the polyhedral hyperbolic discrete problem are derived using the polyhedral nature of the problem. By the discretization method of hyperbolic DFIs, the optimality conditions for the polyhedral discrete approximate problem are formulated in the form of the Mahmudov adjoint inclusions. We establish sufficient optimality conditions for the polyhedral DFIs of hyperbolic type. To the best of our knowledge, these results are new in the literature and use the discretization method when creating the optimality conditions for polyhedral hyperbolic DFIs. This method differs from formerly used methods because of its polyhedral structure.

KW - Laplace operator

KW - discrete-approximation

KW - hyperbolic differential inclusions

KW - optimality conditions

KW - plyhedral

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PB - Institute of Electrical and Electronics Engineers Inc.

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Cicek G, Mahmudov EN. Optimization of the Hyperbolic Type Differential Inclusions Described by Polyhedral Set Valued Mappings. In 2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023. Institute of Electrical and Electronics Engineers Inc. 2023. (2023 5th International Conference on Problems of Cybernetics and Informatics, PCI 2023). doi: 10.1109/PCI60110.2023.10326021

Optimization of the Hyperbolic Type Differential Inclusions Described by Polyhedral Set Valued Mappings

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