Canonical dual least square method for solving general nonlinear systems of quadratic equations

Authors:
N. Ruan;David Y. Gao;Y. Jiao
Affiliations:
Department of Mathematics, Virginia Tech, Blacksburg, USA 24061;Department of Mathematics, Virginia Tech, Blacksburg, USA 24061;Department of Fisheries and Wildlife Sciences, Virginia Tech, Blacksburg, USA 24061
Venue:
Computational Optimization and Applications
Year:
2010

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Abstract

This paper presents a canonical dual approach for solving general nonlinear algebraic systems. By using least square method, the nonlinear system of m-quadratic equations in n-dimensional space is first formulated as a nonconvex optimization problem. We then proved that, by the canonical duality theory developed by the second author, this nonconvex problem is equivalent to a concave maximization problem in 驴 m , which can be solved easily by well-developed convex optimization techniques. Both existence and uniqueness of global optimal solutions are discussed, and several illustrative examples are presented.