Parametric continuation method with correction and its applications
type: Item
instance of: scholarly article
title: Parametric continuation method with correction and its applications
zbMATH Open document ID: 1181.65097
author: S. S. Zhulin
published in: Computational Mathematics and Modeling
publication date: 2009-11-13T00:00:00Z
review text: The main topic of this paper is to develop a reliable computationally efficient method applicable to a wide class of optimal control problems. This method, called parametric continuation method for solving nonlinear algebric and functional equations, is based on homotopy theory (fixed point homotopy, Newton homotopy etc.). Using the parametric continuation method with correction, the author propose a numerical method for solving nonlinear equations. The algorithm proposed, and the main theorem show the quality of approximation of the homotopy curve. Then, the parametric continuation method is applied to solve a nonlinear boundary-value problem for ordinary differential equations, and to find the Pontryagin extremal solution of an optimal control problem by its reduction to a boundary-value problem. Other applications are also discussed: control-nonlinear problems and affine problems with mixed constraints. Maximizer algorithms are proposed and an analytical form of the derivative is obtained.
reviewed by: Iulian Coroian
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65H20
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 49M15
zbMATH DE Number: 5633021
zbMATH Keywords: nonlinear equations
zbMATH Keywords: homotopy theory
zbMATH Keywords: parametric continuation method
zbMATH Keywords: boundary-value problem
zbMATH Keywords: optimal control problem
zbMATH Keywords: Pontryagin maximum principle
zbMATH Keywords: fixed point homotopy
zbMATH Keywords: Newton homotopy
zbMATH Keywords: algorithm
zbMATH Keywords: Pontryagin extremal solution
MaRDI profile type: Publication
full work available at URL: s10598-009-9037-y
OpenAlex ID: W2161994909
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DOI: 10.1007/S10598-009-9037-Y
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description: scientific article; zbMATH DE number 5633021