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A new one-step smoothing Newton method for second-order cone programming

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Abstract

In this paper, we present a new one-step smoothing Newton method for solving the second-order cone programming (SOCP). Based on a new smoothing function of the well-known Fischer-Burmeister function, the SOCP is approximated by a family of parameterized smooth equations. Our algorithm solves only one system of linear equations and performs only one Armijo-type line search at each iteration. It can start from an arbitrary initial point and does not require the iterative points to be in the sets of strictly feasible solutions. Without requiring strict complementarity at the SOCP solution, the proposed algorithm is shown to be globally and locally quadratically convergent under suitable assumptions. Numerical experiments demonstrate the feasibility and efficiency of our algorithm.

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Authors and Affiliations

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

    Jingyong Tang

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

    Jingyong Tang & Li Dong

  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 Systems Science, Taishan University, 271012, Tai’an, P.R.China

    Liang Fang

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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Corresponding author

Correspondence to Li Dong.

Additional information

This work was supported by National Natural Science Foundation of China (10971122), Natural Science Foundation of Shandong Province (Y2008A01), Specialized Research Foundation for the Doctoral Program of Higher Education (20093718110005) and Project of Shandong Province Higher Educational Science and Technology Program (J10LA51).

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Tang, J., He, G., Dong, L. et al. A new one-step smoothing Newton method for second-order cone programming. Appl Math 57, 311–331 (2012). https://doi.org/10.1007/s10492-012-0019-6

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  • DOI: https://doi.org/10.1007/s10492-012-0019-6

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