An Eikonal Equation with Vanishing Lagrangian Arising in Global Optimization

Abstract We show a connection between global unconstrained optimization of continuous function f and weak KAM theory for an eikonal-type equation arising also in ergodic control. A solution v the critical Hamilton–Jacobi is built by small discount approximation as well long time limit associated evolutive equation. Then represented value control problem with target, whose optimal trajectories are driven differential inclusion describing gradient descent . Such proved to converge set minima , using tools occupational measures. prove that some cases reached finite time.