Smoothing Newton method for generalized complementarity problems based on a new smoothing function

In this paper, the generalized complementarity problem is studied. Based on a new smoothing function, the generalized complementarity problem is solved by a smoothing Newton-type algorithm. Under suitable conditions, we prove that the iteration sequence generated by the proposed smoothing method is bounded and the proposed algorithm is globally convergent. Some numerical results are reported.

[1]  Hongwei Liu,et al.  Convergence of a non-interior smoothing method for variational inequality problems , 2012 .

[2]  Roberto Andreani,et al.  On the Resolution of the Generalized Nonlinear Complementarity Problem , 2002, SIAM J. Optim..

[3]  Houduo Qi,et al.  A Regularized Smoothing Newton Method for Box Constrained Variational Inequality Problems with P0-Functions , 1999, SIAM J. Optim..

[4]  Helmut Kleinmichel,et al.  A New Class of Semismooth Newton-Type Methods for Nonlinear Complementarity Problems , 1998, Comput. Optim. Appl..

[5]  Patrick T. Harker,et al.  Smooth Approximations to Nonlinear Complementarity Problems , 1997, SIAM J. Optim..

[6]  Bintong Chen,et al.  A Global Linear and Local Quadratic Noninterior Continuation Method for Nonlinear Complementarity Problems Based on Chen-Mangasarian Smoothing Functions , 1999, SIAM J. Optim..

[7]  Zhenghai Huang,et al.  Predictor-Corrector Smoothing Newton Method, Based on a New Smoothing Function, for Solving the Nonlinear Complementarity Problem with a P0 Function , 2003 .

[8]  Patrick T. Harker,et al.  Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications , 1990, Math. Program..

[9]  A. K. Singh,et al.  Smoothed penalty algorithms for optimization of nonlinear models , 2007, Comput. Optim. Appl..

[10]  Christian Kanzow,et al.  Some Noninterior Continuation Methods for Linear Complementarity Problems , 1996, SIAM J. Matrix Anal. Appl..

[11]  Jian Zhang,et al.  A variant smoothing Newton method for P0-NCP based on a new smoothing function , 2009 .

[12]  Jie Sun,et al.  A smoothing Newton algorithm for the LCP with a sufficient matrix that terminates finitely at a maximally complementary solution , 2006, Optim. Methods Softw..

[13]  Defeng Sun,et al.  A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities , 2000, Math. Program..

[14]  Ahn Byong-hun.  Iterative methods for linear complementarity problems with upperbounds on primary variables , 1983 .

[15]  Zhensheng Yu,et al.  A cosh-based smoothing Newton method for P0 nonlinear complementarity problem , 2011 .

[16]  Changfeng Ma,et al.  A new smoothing and regularization Newton method for P0-NCP , 2010, J. Glob. Optim..

[17]  Defeng Sun,et al.  Sub-quadratic convergence of a smoothing Newton algorithm for the P0– and monotone LCP , 2004, Math. Program..

[18]  Yiju Wang,et al.  A smoothing Newton-type method for generalized nonlinear complementarity problem , 2008 .

[19]  Yiju Wang,et al.  A Nonsmooth L-M Method for Solving the Generalized Nonlinear Complementarity Problem over a Polyhedral Cone , 2005 .

[20]  Zheng-Hai Huang,et al.  Locating a maximally complementary solution of the monotone NCP by using non-interior-point smoothing algorithms , 2005, Math. Methods Oper. Res..

[21]  Christian Kanzow,et al.  On the resolution of monotone complementarity problems , 1996, Comput. Optim. Appl..

[22]  Masao Fukushima,et al.  A Trust Region Method for Solving Generalized Complementarity Problems , 1998, SIAM J. Optim..

[23]  Xiaojun Chen,et al.  A Global and Local Superlinear Continuation-Smoothing Method for P0 and R0 NCP or Monotone NCP , 1999, SIAM J. Optim..

[24]  Bintong Chen,et al.  A Non-Interior-Point Continuation Method for Linear Complementarity Problems , 1993, SIAM J. Matrix Anal. Appl..

[25]  Jiye Han,et al.  The non-interior continuation methods for solving theP0 function nonlinear complementarity problem , 2001 .

[26]  Michael C. Ferris,et al.  Engineering and Economic Applications of Complementarity Problems , 1997, SIAM Rev..