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Application of the Steepest Descent Method to Solving Differential Inclusions with Either Free or Fixed Right End. / Fominyh, Alexander.

2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings. ed. / LN Polyakova. Institute of Electrical and Electronics Engineers Inc., 2017. p. 99-102 7973956.

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

Harvard

Fominyh, A 2017, Application of the Steepest Descent Method to Solving Differential Inclusions with Either Free or Fixed Right End. in LN Polyakova (ed.), 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings., 7973956, Institute of Electrical and Electronics Engineers Inc., pp. 99-102, 2017 Constructive Nonsmooth Analysis and Related Topics, Saint-Petersburg, Russian Federation, 22/05/17. https://doi.org/10.1109/CNSA.2017.7973956

APA

Fominyh, A. (2017). Application of the Steepest Descent Method to Solving Differential Inclusions with Either Free or Fixed Right End. In LN. Polyakova (Ed.), 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings (pp. 99-102). [7973956] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CNSA.2017.7973956

Vancouver

Fominyh A. Application of the Steepest Descent Method to Solving Differential Inclusions with Either Free or Fixed Right End. In Polyakova LN, editor, 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2017. p. 99-102. 7973956 https://doi.org/10.1109/CNSA.2017.7973956

Author

Fominyh, Alexander. / Application of the Steepest Descent Method to Solving Differential Inclusions with Either Free or Fixed Right End. 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings. editor / LN Polyakova. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 99-102

BibTeX

@inproceedings{3258ad34d5604126a5ca3d0d30246430,
title = "Application of the Steepest Descent Method to Solving Differential Inclusions with Either Free or Fixed Right End",
abstract = "In the paper we study a differential inclusion with a given continuous convex multivalued mapping. For a given finite time interval, it is required to construct a solution of the differential inclusion that satisfies the given initial and the final conditions. With the help of support functions, the original problem is reduced to minimizing some functional in the space of partially continuous functions. In the case of continuous differentiability of the support function of a multivalued mapping with respect to the phase variables, this functional is Gateaux differentiable. In the paper, Gateaux gradient is found, necessary and sufficient conditions for the minimum of the given functional are obtained. On the basis of these conditions, the method of the steepest descent is applied to the original problem. Numerical examples illustrate the method realization.",
author = "Alexander Fominyh",
year = "2017",
month = jul,
day = "10",
doi = "10.1109/CNSA.2017.7973956",
language = "Английский",
pages = "99--102",
editor = "LN Polyakova",
booktitle = "2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
address = "Соединенные Штаты Америки",
note = "null ; Conference date: 22-05-2017 Through 27-05-2017",
url = "http://www.mathnet.ru/php/conference.phtml?confid=968&option_lang=rus, http://www.pdmi.ras.ru/EIMI/2017/CNSA/",

}

RIS

TY - GEN

T1 - Application of the Steepest Descent Method to Solving Differential Inclusions with Either Free or Fixed Right End

AU - Fominyh, Alexander

PY - 2017/7/10

Y1 - 2017/7/10

N2 - In the paper we study a differential inclusion with a given continuous convex multivalued mapping. For a given finite time interval, it is required to construct a solution of the differential inclusion that satisfies the given initial and the final conditions. With the help of support functions, the original problem is reduced to minimizing some functional in the space of partially continuous functions. In the case of continuous differentiability of the support function of a multivalued mapping with respect to the phase variables, this functional is Gateaux differentiable. In the paper, Gateaux gradient is found, necessary and sufficient conditions for the minimum of the given functional are obtained. On the basis of these conditions, the method of the steepest descent is applied to the original problem. Numerical examples illustrate the method realization.

AB - In the paper we study a differential inclusion with a given continuous convex multivalued mapping. For a given finite time interval, it is required to construct a solution of the differential inclusion that satisfies the given initial and the final conditions. With the help of support functions, the original problem is reduced to minimizing some functional in the space of partially continuous functions. In the case of continuous differentiability of the support function of a multivalued mapping with respect to the phase variables, this functional is Gateaux differentiable. In the paper, Gateaux gradient is found, necessary and sufficient conditions for the minimum of the given functional are obtained. On the basis of these conditions, the method of the steepest descent is applied to the original problem. Numerical examples illustrate the method realization.

UR - http://www.scopus.com/inward/record.url?scp=85027466696&partnerID=8YFLogxK

U2 - 10.1109/CNSA.2017.7973956

DO - 10.1109/CNSA.2017.7973956

M3 - статья в сборнике материалов конференции

AN - SCOPUS:85027466696

SP - 99

EP - 102

BT - 2017 Constructive Nonsmooth Analysis and Related Topics (Dedicated to the Memory of V.F. Demyanov), CNSA 2017 - Proceedings

A2 - Polyakova, LN

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 22 May 2017 through 27 May 2017

ER -

ID: 18533916