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We propose a new globally convergent numerical method to solveHamilton-Jacobi equations in $\mathbb{R}^d$, $d \geq 1$. This method is namedas the Carleman convexification method. By Carleman convexification, we meanthat we use a Carleman weight function to convexify the conventional leastsquares mismatch functional. We will prove a new version of the convexificationtheorem guaranteeing that the mismatch functional involving the Carleman weightfunction is strictly convex and, therefore, has a unique minimizer. Moreover, aconsequence of our convexification theorem guarantees that the minimizer of theCarleman weighted mismatch functional is an approximation of the viscositysolution we want to compute. Some numerical results in 1D and 2D will bepresented.

The Carleman convexification method for Hamilton-Jacobi equations on the whole space