Penalty Methods for the Solution of Discrete HJB Equations -- Continuous Control and Obstacle Problems
AbstractIn this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. Our results include estimates of the penalisation error for a class of penalty terms, and we show that variations of Newton's method can be used to obtain globally convergent iterative solvers for the penalised equations. Furthermore, we discuss under what conditions local quadratic convergence of the iterative solvers can be expected. We include numerical results demonstrating the competitiveness of our methods.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1105.5954.
Date of creation: May 2011
Date of revision: Dec 2011
Publication status: Published in SIAM J. Numer. Anal. 50(2), 595-625, 2012
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