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A smoothing Newton method for symmetric cone complementarity problem

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Abstract

We first extend a new class of smoothing functions, which contains the well-known Chen-Harker-Kanzow-Smale smoothing function and Huang-Han-Chen smoothing function as special cases, for the nonlinear complementarity problem to the symmetric cone complementarity problem (SCCP). And then we present a smoothing Newton algorithm for the SCCP based on the new class of smoothing functions. Both the existence of Newton directions and the boundedness of the level set are showed for the SCCP with the Cartesian \(P_0\)-property, which contains the monotone SCCP as a special case. The global linear convergence and locally superlinear convergence are established under a nonsingular assumption. Some numerical results for second order cone complementarity problems, a special case of SCCP, show that the proposed algorithm is effective.

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Acknowledgments

The project is supported by the NSF of China (NO.11326188,61105065).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Xidian University, Xi’an, 710071, China

    Lixia Liu, Sanyang Liu & Yan Wu

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  1. Lixia Liu
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  2. Sanyang Liu
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  3. Yan Wu
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Correspondence to Lixia Liu.

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Liu, L., Liu, S. & Wu, Y. A smoothing Newton method for symmetric cone complementarity problem. J. Appl. Math. Comput. 47, 175–191 (2015). https://doi.org/10.1007/s12190-014-0768-3

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  • DOI: https://doi.org/10.1007/s12190-014-0768-3

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