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AIMS Mathematics

2022, Volume 7, Issue 9: 17612-17627. doi: 10.3934/math.2022970
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Research article

New convergence analysis of a class of smoothing Newton-type methods for second-order cone complementarity problem

  • College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China
  • Received: 30 May 2022 Revised: 12 July 2022 Accepted: 21 July 2022 Published: 01 August 2022

  • MSC : 65K05, 90C33

  • In this paper we propose a class of smoothing Newton-type methods for solving the second-order cone complementarity problem (SOCCP). The proposed method design is based on a special regularized Chen-Harker-Kanzow-Smale (CHKS) smoothing function. When the solution set of the SOCCP is nonempty, our method has the following convergence properties: (ⅰ) it generates a bounded iteration sequence; (ⅱ) the value of the merit function converges to zero; (ⅲ) any accumulation point of the generated iteration sequence is a solution of the SOCCP; (ⅳ) it has the local quadratic convergence rate under suitable assumptions. Some numerical results are reported.

    Citation: Li Dong, Jingyong Tang. New convergence analysis of a class of smoothing Newton-type methods for second-order cone complementarity problem[J]. AIMS Mathematics, 2022, 7(9): 17612-17627. doi: 10.3934/math.2022970

    Related Papers:

  • In this paper we propose a class of smoothing Newton-type methods for solving the second-order cone complementarity problem (SOCCP). The proposed method design is based on a special regularized Chen-Harker-Kanzow-Smale (CHKS) smoothing function. When the solution set of the SOCCP is nonempty, our method has the following convergence properties: (ⅰ) it generates a bounded iteration sequence; (ⅱ) the value of the merit function converges to zero; (ⅲ) any accumulation point of the generated iteration sequence is a solution of the SOCCP; (ⅳ) it has the local quadratic convergence rate under suitable assumptions. Some numerical results are reported.


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