A new iterative method for discrete HJB equations
type: Item
instance of: scholarly article
title: A new iterative method for discrete HJB equations
zbMATH Open document ID: 1157.65045
author: Zhanyong Zou
author: Shuzi Zhou
published in: Numerische Mathematik
publication date: 2008-12-01T00:00:00Z
review text: The goal of this paper is to propose a successive relaxation iterative algorithm for discrete Hamilton-Jacobi-Bellman equation: \((1) \max_{1\leq j\leq K} \{A^JU-F^J\}=0\) where \(A^j \in \mathbb R^{n \times n}, F^j \in \mathbb R^n, j=1,2,\dots K\). Equation (1) is a system of nonsmooth nonlinear equations. A successive iterative scheme, similar to the Jacobi iteration for a linear system is presented. Main result: Numerical tests show that the authors' iterative scheme is faster than algorithm A (a simultaneous iterative scheme). It may be a new choice for solving the subproblems of domain decomposition methods for (1). It is also a possible nonlinear smoother if a new multigrid method for (1) is constructed. The new iterative scheme and the convergence theorem (the monotone convergence for the algorithm) are proposed. Finally some theoretical discussions are also presented.
reviewed by: Jan Lovíšek
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 49M27
zbMATH DE Number: 5376043
zbMATH Keywords: elliptic operators of second order
zbMATH Keywords: stochastic control problem
zbMATH Keywords: finite difference method
zbMATH Keywords: algorithm
zbMATH Keywords: supersolution
zbMATH Keywords: successive iterative scheme
zbMATH Keywords: algorithm A
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
zbMATH Keywords: discrete Hamilton-Jacobi-Bellman equation
zbMATH Keywords: Jacobi iteration
zbMATH Keywords: domain decomposition
zbMATH Keywords: multigrid method
MaRDI profile type: Publication
full work available at URL: s00211-008-0166-6
OpenAlex ID: W2034834308
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cites work: A new domain decomposition method for an HJB equation.
DOI: 10.1007/S00211-008-0166-6
description: scientific article; zbMATH DE number 5376043