Global Non-Convex Optimization via Hamilton–Jacobi–Bellman Equations

This talk introduces a novel framework for global optimization based on the Hamilton-Jacobi-Bellman (HJB) equation. We begin by reformulating the global optimization problem as an infinite-horizon optimal control problem. The solution to the associated HJB equation yields a value function that captures the landscape of the objective. By extracting gradient information from this value function, we obtain a feedback control that drives trajectories toward the global minimizers of general non-convex functions. Theoretical results establish explicit convergence rates for both the variational behavior of the value function and the pathwise convergence of the resulting trajectories.