Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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. ред. / LN Polyakova. Institute of Electrical and Electronics Engineers Inc., 2017. стр. 99-102 7973956.Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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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