Optimization of second order evolution differential inclusions problem with phase constraints

Gülseren Çiçek; Elimhan Mahmudov

doi:10.1063/1.5136128

Optimization of second order evolution differential inclusions problem with phase constraints

Gülseren Çiçek, Elimhan Mahmudov

Department of Mathematics Engineering

Istanbul University

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

Abstract

In this paper, we obtain optimality conditions for a problem of convex and non-convex second order evolution differential inclusions with phase constraints. Beginning with second order discrete inclusions problem, we derive necessary and sufficient optimality conditions for the discrete case. We use Locally Dual Mapping definition to derive necessary and sufficient conditions for the optimality of the discrete approximation problem. We prove equivalence theorems in order to obtain a relation between discrete approximation and continuous problems. Passing to the limit, sufficient conditions to the continuous optimal problem are established.

Original language	English
Title of host publication	3rd International Conference of Mathematical Sciences, ICMS 2019
Editors	Huseyin Cakalli, Ljubisa D. R. Kocinac, Robin Harte, Valeria Neves Domingos Cavalcanti, Allaberen Ashyralyev, Izzet Sakalli, Ibrahim Canak, Ozay Gurtug, Marcelo Moreira Cavalcanti, Duran Turkoglu, Mujgan Tez, Hacer Sengul Kandemir, Sahin Uyaver, Kadri Ulas Akay, Ilhan Gul, Temha Erkoc Yilmazturk, Tugba Akyel, Filiz Cagatay Ucgun, Hakan Sahin
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735419308
DOIs	https://doi.org/10.1063/1.5136128
Publication status	Published - 6 Dec 2019
Event	3rd International Conference of Mathematical Sciences, ICMS 2019 - Istanbul, Turkey Duration: 4 Sept 2019 → 8 Sept 2019

Publication series

Name	AIP Conference Proceedings
Volume	2183
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	3rd International Conference of Mathematical Sciences, ICMS 2019
Country/Territory	Turkey
City	Istanbul
Period	4/09/19 → 8/09/19

Bibliographical note

Publisher Copyright:
© 2019 Author(s).

Keywords

evolution
Locally dual mapping
Second order differential inclusion

Access to Document

10.1063/1.5136128

Cite this

Çiçek, G., & Mahmudov, E. (2019). Optimization of second order evolution differential inclusions problem with phase constraints. In H. Cakalli, L. D. R. Kocinac, R. Harte, V. N. D. Cavalcanti, A. Ashyralyev, I. Sakalli, I. Canak, O. Gurtug, M. M. Cavalcanti, D. Turkoglu, M. Tez, H. S. Kandemir, S. Uyaver, K. U. Akay, I. Gul, T. E. Yilmazturk, T. Akyel, F. C. Ucgun, & H. Sahin (Eds.), 3rd International Conference of Mathematical Sciences, ICMS 2019 Article 040008 (AIP Conference Proceedings; Vol. 2183). American Institute of Physics Inc.. https://doi.org/10.1063/1.5136128

Çiçek, Gülseren ; Mahmudov, Elimhan. / Optimization of second order evolution differential inclusions problem with phase constraints. 3rd International Conference of Mathematical Sciences, ICMS 2019. editor / Huseyin Cakalli ; Ljubisa D. R. Kocinac ; Robin Harte ; Valeria Neves Domingos Cavalcanti ; Allaberen Ashyralyev ; Izzet Sakalli ; Ibrahim Canak ; Ozay Gurtug ; Marcelo Moreira Cavalcanti ; Duran Turkoglu ; Mujgan Tez ; Hacer Sengul Kandemir ; Sahin Uyaver ; Kadri Ulas Akay ; Ilhan Gul ; Temha Erkoc Yilmazturk ; Tugba Akyel ; Filiz Cagatay Ucgun ; Hakan Sahin. American Institute of Physics Inc., 2019. (AIP Conference Proceedings).

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abstract = "In this paper, we obtain optimality conditions for a problem of convex and non-convex second order evolution differential inclusions with phase constraints. Beginning with second order discrete inclusions problem, we derive necessary and sufficient optimality conditions for the discrete case. We use Locally Dual Mapping definition to derive necessary and sufficient conditions for the optimality of the discrete approximation problem. We prove equivalence theorems in order to obtain a relation between discrete approximation and continuous problems. Passing to the limit, sufficient conditions to the continuous optimal problem are established.",

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Çiçek, G & Mahmudov, E 2019, Optimization of second order evolution differential inclusions problem with phase constraints. in H Cakalli, LDR Kocinac, R Harte, VND Cavalcanti, A Ashyralyev, I Sakalli, I Canak, O Gurtug, MM Cavalcanti, D Turkoglu, M Tez, HS Kandemir, S Uyaver, KU Akay, I Gul, TE Yilmazturk, T Akyel, FC Ucgun & H Sahin (eds), 3rd International Conference of Mathematical Sciences, ICMS 2019., 040008, AIP Conference Proceedings, vol. 2183, American Institute of Physics Inc., 3rd International Conference of Mathematical Sciences, ICMS 2019, Istanbul, Turkey, 4/09/19. https://doi.org/10.1063/1.5136128

Optimization of second order evolution differential inclusions problem with phase constraints. / Çiçek, Gülseren; Mahmudov, Elimhan.
3rd International Conference of Mathematical Sciences, ICMS 2019. ed. / Huseyin Cakalli; Ljubisa D. R. Kocinac; Robin Harte; Valeria Neves Domingos Cavalcanti; Allaberen Ashyralyev; Izzet Sakalli; Ibrahim Canak; Ozay Gurtug; Marcelo Moreira Cavalcanti; Duran Turkoglu; Mujgan Tez; Hacer Sengul Kandemir; Sahin Uyaver; Kadri Ulas Akay; Ilhan Gul; Temha Erkoc Yilmazturk; Tugba Akyel; Filiz Cagatay Ucgun; Hakan Sahin. American Institute of Physics Inc., 2019. 040008 (AIP Conference Proceedings; Vol. 2183).

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

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AU - Mahmudov, Elimhan

PY - 2019/12/6

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N2 - In this paper, we obtain optimality conditions for a problem of convex and non-convex second order evolution differential inclusions with phase constraints. Beginning with second order discrete inclusions problem, we derive necessary and sufficient optimality conditions for the discrete case. We use Locally Dual Mapping definition to derive necessary and sufficient conditions for the optimality of the discrete approximation problem. We prove equivalence theorems in order to obtain a relation between discrete approximation and continuous problems. Passing to the limit, sufficient conditions to the continuous optimal problem are established.

AB - In this paper, we obtain optimality conditions for a problem of convex and non-convex second order evolution differential inclusions with phase constraints. Beginning with second order discrete inclusions problem, we derive necessary and sufficient optimality conditions for the discrete case. We use Locally Dual Mapping definition to derive necessary and sufficient conditions for the optimality of the discrete approximation problem. We prove equivalence theorems in order to obtain a relation between discrete approximation and continuous problems. Passing to the limit, sufficient conditions to the continuous optimal problem are established.

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KW - Locally dual mapping

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A2 - Cakalli, Huseyin

A2 - Kocinac, Ljubisa D. R.

A2 - Harte, Robin

A2 - Cavalcanti, Valeria Neves Domingos

A2 - Ashyralyev, Allaberen

A2 - Sakalli, Izzet

A2 - Canak, Ibrahim

A2 - Gurtug, Ozay

A2 - Cavalcanti, Marcelo Moreira

A2 - Turkoglu, Duran

A2 - Tez, Mujgan

A2 - Kandemir, Hacer Sengul

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A2 - Akyel, Tugba

A2 - Ucgun, Filiz Cagatay

A2 - Sahin, Hakan

PB - American Institute of Physics Inc.

T2 - 3rd International Conference of Mathematical Sciences, ICMS 2019

Y2 - 4 September 2019 through 8 September 2019

ER -

Çiçek G, Mahmudov E. Optimization of second order evolution differential inclusions problem with phase constraints. In Cakalli H, Kocinac LDR, Harte R, Cavalcanti VND, Ashyralyev A, Sakalli I, Canak I, Gurtug O, Cavalcanti MM, Turkoglu D, Tez M, Kandemir HS, Uyaver S, Akay KU, Gul I, Yilmazturk TE, Akyel T, Ucgun FC, Sahin H, editors, 3rd International Conference of Mathematical Sciences, ICMS 2019. American Institute of Physics Inc. 2019. 040008. (AIP Conference Proceedings). doi: 10.1063/1.5136128

Optimization of second order evolution differential inclusions problem with phase constraints

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