Penalty methods for the solution of discrete HJB equations -- continuous control and obstacle problems
type: Item
instance of: scholarly article
zbMATH Open document ID: 1314.65087
DOI: 10.1137/110835840
author: J. H. Witte
author: C. Reisinger
published in: SIAM Journal on Numerical Analysis
publication date: 2012-08-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1105.5954
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35F21
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 49J55
Mathematics Subject Classification ID: 91B26
Mathematics Subject Classification ID: 91G60
zbMATH DE Number: 6070588
zbMATH Keywords: HJB obstacle problem
zbMATH Keywords: weighted time stepping discretization
zbMATH Keywords: penalty method
zbMATH Keywords: semismooth Newton's method
zbMATH Keywords: discrete Hamilton-Jacobi-Bellman (HJB) equations
zbMATH Keywords: optimal stochastic control
zbMATH Keywords: convergence
zbMATH Keywords: incomplete market investment
zbMATH Keywords: policy iteration
MaRDI profile type: Publication
OpenAlex ID: W3106269269
arXiv ID: 1105.5954
title: Penalty methods for the solution of discrete HJB equations -- continuous control and obstacle problems
review text: The authors present penalty methods for the solution of discrete Hamilton-Jacobi-Bellman (HJB) equations. The paper draws the problem from optimal stochastic control that is formulated and studied in the domain of mathematical analysis/numerical analysis. In particular, the authors start with the formulation of two kinds of nonlinear equations which are solved numerically. The results include estimates of the penalization error for a class of penalty terms. In the proofs they apply variations of Newton's method, in order to obtain globally convergent iterative solvers for the penalized equations. It's interesting that an analysis is provided subject to certain conditions which can guarantee quadratic convergence of the iterative solvers. Numerical evidence is provided with a concrete example on an incomplete market investment problem. An analysis on discrete systems is also included in the present study. The paper concludes with two appendices on policy iteration for the HJB equation and policy iteration for the HJB obstacle problem.
reviewed by: John T. Coletsos
description: scientific article; zbMATH DE number 6070588