Numerical computation of the value function of optimally controlled stochastic switching processes by multi-grid techniques
作者:
Martina Bloβ,
Ronald H. W. Hoppe,
期刊:
Numerical Functional Analysis and Optimization
(Taylor Available online 1989)
卷期:
Volume 10,
issue 3-4
页码: 275-304
ISSN:0163-0563
年代: 1989
DOI:10.1080/01630568908816304
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
By the dynamic programming principle the value function of an optimally controlled stochasticswitching process can be shown to satisfy a boundary value problem for a fully nonlinear second-order elliptic differential equation of Hamilton-Jacobi-Bellman (HJB-) type. For the numerical solution of that HJB-equation we present a multi-grid algorithm whose main features arethe use of nonlinear Gauss-Seidel iteration in the smoothing process and an adaptive local choice of prolongations and restrictions in the coarse-to-fine and fine-to-coarse transfers. Local convergence is proved by combining nonlinear multi-grid convergence theory and elementarysubdifferential calculus. The efficiency of the algorithm is demonstrated for optimal advertising in stochastic dynamic sales response models of Vidale-Wolfe type.
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