PENALTY METHODS FOR THE SOLUTION OF DISCRETE HJB EQUATIONS-CONTINUOUS CONTROL AND OBSTACLE PROBLEMS

Journal article

In 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 penalization 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 penalized 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. © 2012 Society for Industrial and Applied Mathematics.

Authors: Witte, J; Reisinger, C

• Publication status: Published
• Journal: SIAM JOURNAL ON NUMERICAL ANALYSIS
• Volume: 50
• Issue: 2
• Pages: 595-625
• Publication date: 2012-01-01
• DOI: 10.1137/110835840
• EISSN: 1095-7170
• ISSN: 0036-1429
• Language: English
• Keywords: min-max problem; HJB equation; semismooth Newton method; penalty method; numerical solution; viscosity solution; HJB obstacle problem