Abstract
In this chapter we briefly outline a new and remarkably fast algorithm for solving a large class of high dimensional Hamilton-Jacobi (H-J) initial value problems arising in optimal control and elsewhere [1]. This is done without the use of grids or numerical approximations. Moreover, by using the level set method [8] we can rapidly compute projections of a point in \(\mathbb{R}^{n}\), n large to a fairly arbitrary compact set [2]. The method seems to generalize widely beyond what will we present here to some nonconvex Hamiltonians, new linear programming algorithms, differential games, and perhaps state dependent Hamiltonians.
Keywords
- Nonconvex Hamiltonians
- Linear Programming Algorithm
- Differential Games
- Initial Value Problem
- Hopf Formula
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
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Acknowledgements
Research supported by ONR grants N000141410683, N000141210838 and DOE grant DE-SC00183838.
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Darbon, J., Osher, S.J. (2016). Splitting Enables Overcoming the Curse of Dimensionality. In: Glowinski, R., Osher, S., Yin, W. (eds) Splitting Methods in Communication, Imaging, Science, and Engineering. Scientific Computation. Springer, Cham. https://doi.org/10.1007/978-3-319-41589-5_12
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DOI: https://doi.org/10.1007/978-3-319-41589-5_12
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