The Duality of Convex Optimization Problem for Differential Inclusions

Sevilay Demir Sağlam; Elimhan N. Mahmudov

doi:10.1063/5.0117079

The Duality of Convex Optimization Problem for Differential Inclusions

Sevilay Demir Sağlam^*, Elimhan N. Mahmudov

^*Corresponding author for this work

Department of Mathematics Engineering

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

Abstract

The purpose of this paper is to investigate the duality for optimal control problems with higher-order differential inclusions. Using locally adjoint mappings and the discretization method, we derive the conditions of optimality for a boundary-value problem with higher-order differential inclusions. This method connects a duality relation problem to a continuous concerning problem. Then, thanks to the dual operations of addition and infimal convolution of convex functions, we obtain duality results. In general, the construction of the duality problem with the assistance of discrete and discrete approximation problems necessitates a significant amount of effort to comprehend the computational aspects. Finally, we show that the optimal solutions to the primal convex and dual concave problems are the same.

Original language	English
Title of host publication	5th International Conference of Mathematical Sciences, ICMS 2021
Editors	Huseyin Cakalli, Ljubisa D. R. Kocinac, Allaberen Ashyralyev, Robin Harte, Mehmet Dik, Ibrahim Canak, Hacer Sengul Kandemir, Mujgan Tez, Ozay Gurtug, Ekrem Savas, Nazlim Deniz Aral, Filiz Cagatay Ucgan, Onder Sahinaslan, Charyyar Ashyralyyev, Sefa Anil Sezer, Arap Duran Turkoglu, Oruc Raif Onvural, Hakan Sahin
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735442580
DOIs	https://doi.org/10.1063/5.0117079
Publication status	Published - 7 Nov 2022
Event	5th International Conference of Mathematical Sciences, ICMS 2021 - Istanbul, Turkey Duration: 23 Jun 2021 → 27 Jun 2021

Publication series

Name	AIP Conference Proceedings
Volume	2483
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	5th International Conference of Mathematical Sciences, ICMS 2021
Country/Territory	Turkey
City	Istanbul
Period	23/06/21 → 27/06/21

Bibliographical note

Publisher Copyright:
© 2022 American Institute of Physics Inc.. All rights reserved.

Keywords

Boundary-value Problem
Duality
Locally adjoint mappings
Transversality

Access to Document

10.1063/5.0117079

Cite this

Sağlam, S. D., & Mahmudov, E. N. (2022). The Duality of Convex Optimization Problem for Differential Inclusions. In H. Cakalli, L. D. R. Kocinac, A. Ashyralyev, R. Harte, M. Dik, I. Canak, H. S. Kandemir, M. Tez, O. Gurtug, E. Savas, N. D. Aral, F. C. Ucgan, O. Sahinaslan, C. Ashyralyyev, S. A. Sezer, A. D. Turkoglu, O. R. Onvural, & H. Sahin (Eds.), 5th International Conference of Mathematical Sciences, ICMS 2021 Article 030013 (AIP Conference Proceedings; Vol. 2483). American Institute of Physics Inc.. https://doi.org/10.1063/5.0117079

Sağlam, Sevilay Demir ; Mahmudov, Elimhan N. / The Duality of Convex Optimization Problem for Differential Inclusions. 5th International Conference of Mathematical Sciences, ICMS 2021. editor / Huseyin Cakalli ; Ljubisa D. R. Kocinac ; Allaberen Ashyralyev ; Robin Harte ; Mehmet Dik ; Ibrahim Canak ; Hacer Sengul Kandemir ; Mujgan Tez ; Ozay Gurtug ; Ekrem Savas ; Nazlim Deniz Aral ; Filiz Cagatay Ucgan ; Onder Sahinaslan ; Charyyar Ashyralyyev ; Sefa Anil Sezer ; Arap Duran Turkoglu ; Oruc Raif Onvural ; Hakan Sahin. American Institute of Physics Inc., 2022. (AIP Conference Proceedings).

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title = "The Duality of Convex Optimization Problem for Differential Inclusions",

abstract = "The purpose of this paper is to investigate the duality for optimal control problems with higher-order differential inclusions. Using locally adjoint mappings and the discretization method, we derive the conditions of optimality for a boundary-value problem with higher-order differential inclusions. This method connects a duality relation problem to a continuous concerning problem. Then, thanks to the dual operations of addition and infimal convolution of convex functions, we obtain duality results. In general, the construction of the duality problem with the assistance of discrete and discrete approximation problems necessitates a significant amount of effort to comprehend the computational aspects. Finally, we show that the optimal solutions to the primal convex and dual concave problems are the same.",

keywords = "Boundary-value Problem, Duality, Locally adjoint mappings, Transversality",

author = "Sağlam, {Sevilay Demir} and Mahmudov, {Elimhan N.}",

note = "Publisher Copyright: {\textcopyright} 2022 American Institute of Physics Inc.. All rights reserved.; 5th International Conference of Mathematical Sciences, ICMS 2021 ; Conference date: 23-06-2021 Through 27-06-2021",

year = "2022",

month = nov,

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doi = "10.1063/5.0117079",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Huseyin Cakalli and Kocinac, {Ljubisa D. R.} and Allaberen Ashyralyev and Robin Harte and Mehmet Dik and Ibrahim Canak and Kandemir, {Hacer Sengul} and Mujgan Tez and Ozay Gurtug and Ekrem Savas and Aral, {Nazlim Deniz} and Ucgan, {Filiz Cagatay} and Onder Sahinaslan and Charyyar Ashyralyyev and Sezer, {Sefa Anil} and Turkoglu, {Arap Duran} and Onvural, {Oruc Raif} and Hakan Sahin",

booktitle = "5th International Conference of Mathematical Sciences, ICMS 2021",

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Sağlam, SD & Mahmudov, EN 2022, The Duality of Convex Optimization Problem for Differential Inclusions. in H Cakalli, LDR Kocinac, A Ashyralyev, R Harte, M Dik, I Canak, HS Kandemir, M Tez, O Gurtug, E Savas, ND Aral, FC Ucgan, O Sahinaslan, C Ashyralyyev, SA Sezer, AD Turkoglu, OR Onvural & H Sahin (eds), 5th International Conference of Mathematical Sciences, ICMS 2021., 030013, AIP Conference Proceedings, vol. 2483, American Institute of Physics Inc., 5th International Conference of Mathematical Sciences, ICMS 2021, Istanbul, Turkey, 23/06/21. https://doi.org/10.1063/5.0117079

The Duality of Convex Optimization Problem for Differential Inclusions. / Sağlam, Sevilay Demir; Mahmudov, Elimhan N.
5th International Conference of Mathematical Sciences, ICMS 2021. ed. / Huseyin Cakalli; Ljubisa D. R. Kocinac; Allaberen Ashyralyev; Robin Harte; Mehmet Dik; Ibrahim Canak; Hacer Sengul Kandemir; Mujgan Tez; Ozay Gurtug; Ekrem Savas; Nazlim Deniz Aral; Filiz Cagatay Ucgan; Onder Sahinaslan; Charyyar Ashyralyyev; Sefa Anil Sezer; Arap Duran Turkoglu; Oruc Raif Onvural; Hakan Sahin. American Institute of Physics Inc., 2022. 030013 (AIP Conference Proceedings; Vol. 2483).

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

TY - GEN

T1 - The Duality of Convex Optimization Problem for Differential Inclusions

AU - Sağlam, Sevilay Demir

AU - Mahmudov, Elimhan N.

PY - 2022/11/7

Y1 - 2022/11/7

N2 - The purpose of this paper is to investigate the duality for optimal control problems with higher-order differential inclusions. Using locally adjoint mappings and the discretization method, we derive the conditions of optimality for a boundary-value problem with higher-order differential inclusions. This method connects a duality relation problem to a continuous concerning problem. Then, thanks to the dual operations of addition and infimal convolution of convex functions, we obtain duality results. In general, the construction of the duality problem with the assistance of discrete and discrete approximation problems necessitates a significant amount of effort to comprehend the computational aspects. Finally, we show that the optimal solutions to the primal convex and dual concave problems are the same.

AB - The purpose of this paper is to investigate the duality for optimal control problems with higher-order differential inclusions. Using locally adjoint mappings and the discretization method, we derive the conditions of optimality for a boundary-value problem with higher-order differential inclusions. This method connects a duality relation problem to a continuous concerning problem. Then, thanks to the dual operations of addition and infimal convolution of convex functions, we obtain duality results. In general, the construction of the duality problem with the assistance of discrete and discrete approximation problems necessitates a significant amount of effort to comprehend the computational aspects. Finally, we show that the optimal solutions to the primal convex and dual concave problems are the same.

KW - Boundary-value Problem

KW - Duality

KW - Locally adjoint mappings

KW - Transversality

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U2 - 10.1063/5.0117079

DO - 10.1063/5.0117079

M3 - Conference contribution

AN - SCOPUS:85142512254

T3 - AIP Conference Proceedings

BT - 5th International Conference of Mathematical Sciences, ICMS 2021

A2 - Cakalli, Huseyin

A2 - Kocinac, Ljubisa D. R.

A2 - Ashyralyev, Allaberen

A2 - Harte, Robin

A2 - Dik, Mehmet

A2 - Canak, Ibrahim

A2 - Kandemir, Hacer Sengul

A2 - Tez, Mujgan

A2 - Gurtug, Ozay

A2 - Savas, Ekrem

A2 - Aral, Nazlim Deniz

A2 - Ucgan, Filiz Cagatay

A2 - Sahinaslan, Onder

A2 - Ashyralyyev, Charyyar

A2 - Sezer, Sefa Anil

A2 - Turkoglu, Arap Duran

A2 - Onvural, Oruc Raif

A2 - Sahin, Hakan

PB - American Institute of Physics Inc.

T2 - 5th International Conference of Mathematical Sciences, ICMS 2021

Y2 - 23 June 2021 through 27 June 2021

ER -

Sağlam SD, Mahmudov EN. The Duality of Convex Optimization Problem for Differential Inclusions. In Cakalli H, Kocinac LDR, Ashyralyev A, Harte R, Dik M, Canak I, Kandemir HS, Tez M, Gurtug O, Savas E, Aral ND, Ucgan FC, Sahinaslan O, Ashyralyyev C, Sezer SA, Turkoglu AD, Onvural OR, Sahin H, editors, 5th International Conference of Mathematical Sciences, ICMS 2021. American Institute of Physics Inc. 2022. 030013. (AIP Conference Proceedings). doi: 10.1063/5.0117079

The Duality of Convex Optimization Problem for Differential Inclusions

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Keywords

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