A method for finding all roots of a system of nonlinear equations is described. Our method makes use of C-GRASP, a recently proposed continuous global optimization heuristic. Given a nonlinear system, we solve a corresponding adaptively modified global optimization problem multiple times, each time using C-GRASP, with areas of repulsion around roots that have already been found. The heuristic makes no use of derivative information. We illustrate the approach on systems from the literature.
AT&T Labs Research Technical Report TD-6V6JCX, Shannon Laboratory, Florham Park, NJ 07932, November 2006.