Strong convergence properties of a modified nonmonotone smoothing algorithm for the SCCP |
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Authors: | Jingyong Tang Jinchuan Zhou Liang Fang |
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Affiliation: | 1.College of Mathematics and Information Science,Xinyang Normal University,Xinyang,China;2.Department of Mathematics, School of Science,Shandong University of Technology,Zibo,China;3.College of Mathematics and System Science,Taishan University,Tai’an,China |
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Abstract: | The smoothing algorithms have been successfully applied to solve the symmetric cone complementarity problem (denoted by SCCP), which in general have the global and local superlinear/quadratic convergence if the solution set of the SCCP is nonempty and bounded. Huang, Hu and Han [Science in China Series A: Mathematics, 52: 833–848, 2009] presented a nonmonotone smoothing algorithm for solving the SCCP, whose global convergence is established by just requiring that the solution set of the SCCP is nonempty. In this paper, we propose a new nonmonotone smoothing algorithm for solving the SCCP by modifying the version of Huang-Hu-Han’s algorithm. We prove that the modified nonmonotone smoothing algorithm not only is globally convergent but also has local superlinear/quadratical convergence if the solution set of the SCCP is nonempty. This convergence result is stronger than those obtained by most smoothing-type algorithms. Finally, some numerical results are reported. |
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