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A Damped Gauss-Newton Method for the Second-Order Cone Complementarity Problem

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Abstract

We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem (SOCCP) as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of the B-subdifferential at a solution being nonsingular. In addition, for the induced FB merit function, we establish its coerciveness and provide a weaker condition than Chen and Tseng (Math. Program. 104:293–327, 2005) for each stationary point to be a solution, under suitable Cartesian P-properties of the involved mapping. By this, a damped Gauss-Newton method is proposed, and the global and superlinear convergence results are obtained. Numerical results are reported for the second-order cone programs from the DIMACS library, which verify the good theoretical properties of the method.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China University of Technology, Guangzhou, 510640, China

    Shaohua Pan

  2. Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan

    Jein-Shan Chen

Authors
  1. Shaohua Pan
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  2. Jein-Shan Chen
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Corresponding author

Correspondence to Shaohua Pan.

Additional information

S. Pan’s work is partially supported by the Doctoral Starting-up Foundation (B13B6050640) of GuangDong Province.

J.-S. Chen is member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. J.-S. Chen’s work is partially supported by National Science Council of Taiwan.

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Pan, S., Chen, JS. A Damped Gauss-Newton Method for the Second-Order Cone Complementarity Problem. Appl Math Optim 59, 293–318 (2009). https://doi.org/10.1007/s00245-008-9054-9

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