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This article proposes a new capture basin algorithm for computing the numerical solution of a class of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs), based on a Lax-Hopf formula. The capture basin algorithm is derived and implemented to perform numerical computations of constrained solutions. The rate of convergence of this first order algorithm is assessed experimentally using an analytical benchmark problem. Finally, its performance is measured with highway data obtained for interstate 180 in California.