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

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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 ℝm, 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.

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Authors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    N. Ruan & David Y. Gao

  2. Department of Fisheries and Wildlife Sciences, Virginia Tech, Blacksburg, VA, 24061, USA

    Y. Jiao

Authors
  1. N. Ruan
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  2. David Y. Gao
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  3. Y. Jiao
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Correspondence to David Y. Gao.

Additional information

Research supported by NSF Grant CCF-0514768.

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Ruan, N., Gao, D.Y. & Jiao, Y. Canonical dual least square method for solving general nonlinear systems of quadratic equations. Comput Optim Appl 47, 335–347 (2010). https://doi.org/10.1007/s10589-008-9222-5

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  • DOI: https://doi.org/10.1007/s10589-008-9222-5

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