Solving systems of nonlinear equations with continuous GRASP

Michael J. Hirsch (mjh8787ufl.edu)
Panos M. Pardalos (pardalosufl.edu)
Mauricio G. C. Resende (mgcrresearch.att.com)

Abstract: 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.

Keywords: Nonlinear systems of equations, global optimization, continuous optimization, heuristic, stochastic algorithm, stochastic local search, nonlinear programming, GRASP, C-GRASP.

Category 1: Global Optimization

Category 2: Global Optimization (Stochastic Approaches )

Category 3: Combinatorial Optimization (Meta Heuristics )

Citation: AT&T Labs Research Technical Report TD-6V6JCX, Shannon Laboratory, Florham Park, NJ 07932, November 2006.

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Entry Submitted: 11/02/2006
Entry Accepted: 11/02/2006
Entry Last Modified: 11/02/2006

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