A discussion of some algorithms for Hamilton-Jacobi equations in density space I

Yat Tin Chow
University of California, Los Angeles (UCLA)
Mathematics Department

In the lectures, we discuss some numerical methods for Hamilton-Jacobi equations in density space which arises in optimal transport and variational/potential mean field games. We start from the optimal control in density space, and arrive at several equivalent formulations of the problem. We then move to discretization, and apply several optimization techniques that may approach the several formulations, e.g.
fixed-point methods, Newton's method, primal-dual hybrid gradient,
(coordinate) descent methods.

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