A smoothing Newton method for symmetric cone complementarity problem

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• 作者：Lixia Liu (1)
  Sanyang Liu (1)
  Yan Wu (1)
  
  1. Department of Mathematics and Statistics ; Xidian University ; Xi鈥檃n ; 710071 ; China
  
• 关键词：Symmetric cone ; Complementarity problem ; Cartesian $$P_0$$ P 0 ; property ; Smoothing Newton method ; Coerciveness ; 90C25 ; 90C30 ; 90C51
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：47
• 期：1-2
• 页码：175-191
• 全文大小：224 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Theory of Computation
  Mathematics of Computing
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1865-2085

文摘

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.