A system and method for solving a set of optimization problems initializes a current region of solutions for the set of optimization problems, performs a reduction phase, and provides the optimal solutions within the current region. The reduction phase creates a random sample of points within the current region and identifies a subregion of the current region that very likely does not contain any optimal solutions. The identified subregion is then removed from the current region. If the current region does not satisfies one or more convergence criteria, the process loops back to create another random sample of points and repeats the above-described steps. If, however, the current region does satisfy the convergence criteria, the optimal solutions within the current region are provided to the output device.