Application of the steepest descent method to solve differential inequalities
Date
2017-10-04
Authors
Fominyh, Alexander V.
Karelin, Vladimir V.
Polyakova, Lyudmila N.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Differential inequalities, Gateaux gradient, Steepest descent method
Citation
Fominyh, A. V., Karelin, V. V., & Polyakova, L. N. (2017). Application of the steepest descent method to solve differential inequalities. <i>Electronic Journal of Differential Equations, 2017</i>(241), pp. 1-8.
Rights
Attribution 4.0 International