Journal article

Perspectives on Characteristics Based Curse-of-Dimensionality-Free Numerical Approaches for Solving Hamilton–Jacobi Equations

I Yegorov, PM Dower

Applied Mathematics & Optimization | Springer New York LLC | Published : 2018


© 2018, Springer Science+Business Media, LLC, part of Springer Nature. This paper extends the considerations of the works (Darbon and Osher, Res Math Sci 3:19, 2016; Chow et al., 2017, regarding curse-of-dimensionality-free numerical approaches to solve certain types of Hamilton–Jacobi equations arising in optimal control problems, differential games and elsewhere. A rigorous formulation and justification for the extended Hopf–Lax formula of(Chow et al., 2017, is provided together with novel theoretical and practical discussions including useful recommendations. By using the method of characteristics, the solutions of some problem classes u..

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