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This is a Experimental Study study.

October 20, 2025Open Access

Policy iteration for nonconvex viscous Hamilton--Jacobi equations

Key Points

Policy iteration achieves exponential convergence rates for nonconvex viscous Hamilton–Jacobi equations.
The study highlights discretization error impacts in uncontrolled diffusion scenarios.
A discrete space-time scheme is utilized to analyze convergence rates effectively.
Implications point to potential advancements in solving complex nonconvex equations.

Abstract

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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Cite This Study

Guo et al. (Mon,) studied this question.

synapsesocial.com/papers/68f64fbb2509bc8625bfb125 https://doi.org/https://doi.org/10.48550/arxiv.2503.02159

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