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In this paper, the authors present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. The results include estimates of the penalisation error for a class of penalty terms, and they show that variations of Newton's method can be used to obtain globally convergent iterative solvers for the penalised equations. Furthermore, they discuss under what conditions local quadratic convergence of the iterative solvers can be expected. They include numerical results demonstrating the competitiveness of the methods.
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