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Computing tasks may often be posed as optimization problems. The objectivefunctions for real-world scenarios are often nonconvex and/ornondifferentiable. State-of-the-art methods for solving these problemstypically only guarantee convergence to local minima. This work presentsHamilton-Jacobi-based Moreau Adaptive Descent (HJ-MAD), a zero-order algorithmwith guaranteed convergence to global minima, assuming continuity of theobjective function. The core idea is to compute gradients of the Moreauenvelope of the objective (which is "piece-wise convex") with adaptivesmoothing parameters. Gradients of the Moreau envelope \rev{(\ie proximaloperators)} are approximated via the Hopf-Lax formula for the viscousHamilton-Jacobi equation. Our numerical examples illustrate global convergence.

Global Solutions to Nonconvex Problems by Evolution of Hamilton-Jacobi PDEs