Application of the steepest descent method to solve differential inequalities

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Application of the steepest descent method to solve differential inequalities. / Fominyh, Alexander V.; Karelin, Vladimir V.; Polyakova, Lyudmila N.

In: Electronic Journal of Differential Equations, Vol. 2017, 241, 04.10.2017.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{4052038e5da2453eb6c6001b3abcd9e9,

title = "Application of the steepest descent method to solve differential inequalities",

abstract = "In this article we consider the problem of finding the solution of a system of differential inequalities. We reduce the original problem to the unconstrained minimization of a functional. We find the Gateaux gradient for this functional, and then obtain nucessary and sufficient conditions for the existence of a minimum. Based on these conditions we apply the steepest descent method, and present a numerical implementation of the method.",

keywords = "Differential inequalities, Gateaux gradient, Steepest descent metho",

author = "Fominyh, {Alexander V.} and Karelin, {Vladimir V.} and Polyakova, {Lyudmila N.}",

year = "2017",

month = oct,

day = "4",

language = "English",

volume = "2017",

journal = "Electronic Journal of Differential Equations",

issn = "1072-6691",

publisher = "Texas State University - San Marcos",

}

RIS

TY - JOUR

T1 - Application of the steepest descent method to solve differential inequalities

AU - Fominyh, Alexander V.

AU - Karelin, Vladimir V.

AU - Polyakova, Lyudmila N.

PY - 2017/10/4

Y1 - 2017/10/4

N2 - In this article we consider the problem of finding the solution of a system of differential inequalities. We reduce the original problem to the unconstrained minimization of a functional. We find the Gateaux gradient for this functional, and then obtain nucessary and sufficient conditions for the existence of a minimum. Based on these conditions we apply the steepest descent method, and present a numerical implementation of the method.

AB - In this article we consider the problem of finding the solution of a system of differential inequalities. We reduce the original problem to the unconstrained minimization of a functional. We find the Gateaux gradient for this functional, and then obtain nucessary and sufficient conditions for the existence of a minimum. Based on these conditions we apply the steepest descent method, and present a numerical implementation of the method.

KW - Differential inequalities

KW - Gateaux gradient

KW - Steepest descent metho

UR - http://www.scopus.com/inward/record.url?scp=85031493367&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85031493367

VL - 2017

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

SN - 1072-6691

M1 - 241

ER -

ID: 18533879