The non-interior continuation methods for solving theP0 function nonlinear complementarity problem

In this paper, we propose a new smooth function that possesses a property not satisfied by the existing smooth functions. Based on this smooth function, we discuss the existence and continuity of the smoothing path for solving theP0 function nonlinear complementarity problem ( NCP). Using the characteristics of the new smooth function, we investigate the boundedness of the iteration sequence generated by the non-interior continuation methods for solving theP0 function NCP under the assumption that the solution set of the NCP is nonempty and bounded. We show that the assumption that the solution set of the NCP is nonempty and bounded is weaker than those required by a few existing continuation methods for solving the NCP

[1]  A. Fischer.  A special newton-type optimization method , 1992 .

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

[3]  Xiaojun Chen,et al.  A parameterized Newton method and a quasi-Newton method for nonsmooth equations , 1994, Comput. Optim. Appl..

[4]  S. Dirkse,et al.  A Comparison of Algorithms for Large Scale Mixed Complementarity Problems , 1995 .

[5]  J. J. Moré,et al.  Smoothing of mixed complementarity problems , 1995 .

[6]  Olvi L. Mangasarian,et al.  A class of smoothing functions for nonlinear and mixed complementarity problems , 1996, Comput. Optim. Appl..

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

[8]  Michael C. Ferris,et al.  A Comparison of Large Scale Mixed Complementarity Problem Solvers , 1997, Comput. Optim. Appl..

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

[10]  Christian Kanzow,et al.  A new approach to continuation methods for complementarity problems with uniform P-functions , 1997, Oper. Res. Lett..

[11]  Vyacheslav Kalashnikov,et al.  Exceptional Families, Topological Degree and Complementarity Problems , 1997, J. Glob. Optim..

[12]  P. Tseng.  Analysis Of A Non-Interior Continuation Method Based On Chen-Mangasarian Smoothing Functions For Com , 1998 .

[13]  James V. Burke,et al.  The Global Linear Convergence of a Noninterior Path-Following Algorithm for Linear Complementarity Problems , 1998, Math. Oper. Res..

[14]  Patrick T. Harker,et al.  Continuation method for nonlinear complementarity problems via normal maps , 1999, Eur. J. Oper. Res..

[15]  Mohamed A. Tawhid,et al.  Existence and Limiting Behavior of Trajectories Associated with P0-equations , 1999, Comput. Optim. Appl..

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

[17]  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..

[18]  D. Sun.  A Regularization Newton Method for Solving Nonlinear Complementarity Problems , 1999 .

[19]  F. Facchinei,et al.  Beyond Monotonicity in Regularization Methods for Nonlinear Complementarity Problems , 1999 .

[20]  Houduo Qi,et al.  Exceptional Families and Existence Theorems for Variational Inequality Problems , 1999 .

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

[22]  M. Seetharama Gowda,et al.  Regularization of P[sub 0]-Functions in Box Variational Inequality Problems , 2000, SIAM J. Optim..