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

^*Bu çalışma için yazışmadan sorumlu yazar

Matematik Bölümü

Araştırma sonucu: ???type-name??? › Konferans katkısı › bilirkişi

Özet

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.

Orijinal dil	İngilizce
Ana bilgisayar yayını başlığı	5th International Conference of Mathematical Sciences, ICMS 2021
Editörler	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
Yayınlayan	American Institute of Physics Inc.
ISBN (Elektronik)	9780735442580
DOI'lar	https://doi.org/10.1063/5.0117079
Yayın durumu	Yayınlandı - 7 Kas 2022
Etkinlik	5th International Conference of Mathematical Sciences, ICMS 2021 - Istanbul, Turkey Süre: 23 Haz 2021 → 27 Haz 2021

Yayın serisi

Adı	AIP Conference Proceedings
Hacim	2483
ISSN (Basılı)	0094-243X
ISSN (Elektronik)	1551-7616

???event.eventtypes.event.conference???

???event.eventtypes.event.conference???	5th International Conference of Mathematical Sciences, ICMS 2021
Ülke/Bölge	Turkey
Şehir	Istanbul
Periyot	23/06/21 → 27/06/21

Bibliyografik not

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

Belgeye Erişim

10.1063/5.0117079

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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 Makale 030013 (AIP Conference Proceedings; Hac. 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. editör / 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).

@inproceedings{434fc68a50644c608d582102ffd73f56,

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,

day = "7",

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",

}

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, hac. 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; Hac. 2483).

Araştırma sonucu: ???type-name??? › Konferans katkısı › bilirkişi

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, editörler, 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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