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A smoothing Newton method for the second-order cone complementarity problem

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Abstract

In this paper we introduce a new smoothing function and show that it is coercive under suitable assumptions. Based on this new function, we propose a smoothing Newton method for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution to the SOCCP. Furthermore, we prove that the generated sequence is bounded if the solution set of the SOCCP is nonempty and bounded. Under the assumption of nonsingularity, we establish the local quadratic convergence of the algorithm without the strict complementarity condition. Numerical results indicate that the proposed algorithm is promising.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Xinyang Normal University, 464000, Xinyang, P.R.China

    Jingyong Tang

  2. Department of Mathematics, Shanghai Jiaotong University, 200240, Shanghai, P.R.China

    Jingyong Tang

  3. College of Information Science and Engineering, Shandong University of Science and Technology, 266510, Qingdao, P.R.China

    Guoping He

  4. College of Mathematics and Information Science, Xinyang Normal University, 464000, Xinyang, P.R.China

    Li Dong

  5. College of Mathematics and Systems Science, Taishan University, 271012, Tai’an, P.R.China

    Liang Fang

  6. Department of Mathematics, School of Science, Shandong University of Technology, 255049, Zibo, P.R.China

    Jinchuan Zhou

Authors
  1. Jingyong Tang
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  2. Guoping He
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  3. Li Dong
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  4. Liang Fang
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  5. Jinchuan Zhou
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Corresponding author

Correspondence to Jingyong Tang.

Additional information

This paper was partly supported by the Project of Shandong Province Higher Educational Science and Technology Program (J10LA51), National Natural Science Foundation of China (10971122, 11101248), and Excellent Young Scientist Foundation of Shandong Province (BS2011SF024).

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Tang, J., He, G., Dong, L. et al. A smoothing Newton method for the second-order cone complementarity problem. Appl Math 58, 223–247 (2013). https://doi.org/10.1007/s10492-013-0011-9

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  • DOI: https://doi.org/10.1007/s10492-013-0011-9

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