Multi-grid methods for Hamilton-Jacobi-Bellman equations
Numerische Mathematik
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations
SIAM Journal on Numerical Analysis
On application of an alternating direction method to Hamilton-Jacobin-Bellman equations
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on boundary and interior layers - computational and asymptotic methods (BAIL 2002)
A new iterative method for discrete HJB equations
Numerische Mathematik
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In this paper, some semismooth methods are considered to solve a nonsmooth equation which can arise from a discrete version of the well-known Hamilton-Jacobi-Bellman equation. By using the slant differentiability introduced by Chen, Nashed and Qi in 2000, a semismooth Newton method is proposed. The method is proved to have monotone convergence by suitably choosing the initial iterative point and local superlinear convergence rate. Moreover, an inexact version of the proposed method is introduced, which reduces the cost of computations and still preserves nice convergence properties. Some numerical results are also reported.