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Policy iteration for nonconvex viscous Hamilton--Jacobi equations

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arxiv 2503.02159 v1 pith:W5UW5OE7 submitted 2025-03-04 math.NA cs.NAmath.APmath.OC

Xiaoqin Guo , Hung Vinh Tran , Yuming Paul Zhang This is my paper · ORCID
classification math.NAcs.NAmath.APmath.OC
keywords hamilton--jacobiviscousdiscreteequationsiterationnonconvexpolicyspace-time
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We study the convergence rates of policy iteration (PI) for nonconvex viscous Hamilton--Jacobi equations using a discrete space-time scheme, where both space and time variables are discretized. We analyze the case with an uncontrolled diffusion term, which corresponds to a possibly degenerate viscous Hamilton--Jacobi equation. We first obtain an exponential convergent result of PI for the discrete space-time schemes. We then investigate the discretization error.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Beyond separability: convergence rate of vanishing viscosity approximations to mean field games via FBSDE stability

    math.OC 2025-05 conditional novelty 7.0 of 10

    The vanishing viscosity approximation to nonlocal, possibly non-separable mean field games converges at rate O(β) in L∞ on compact sets, matching the classical Hamilton-Jacobi rate.

  2. Solving nonconvex Hamilton--Jacobi--Isaacs equations with PINN-based policy iteration

    math.NA 2025-07 conditional novelty 6.0 of 10

    A PINN-based policy iteration method for nonconvex Hamilton-Jacobi-Isaacs equations with a convergence analysis and tests up to 10 dimensions.

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