Numerical Experiments for a Class of Squared Smoothing Newton Methods for Box Constrained Variational Inequality Problems

In this paper we present a class of squared smoothing Newton methods for the box constrained variational inequality problem. This class of squared smoothing Newton methods is a regularized version of the class of smoothing Newton methods proposed in [25]. We tested all the test problem collections of GAMSLIB and MCPLIB with all available starting points. Numerical results indicate that these squared smoothing Newton methods are extremely robust and promising.

[1]  R. Mifflin.  Semismooth and Semiconvex Functions in Constrained Optimization , 1977 .

[2]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[3]  L. Grippo,et al.  A nonmonotone line search technique for Newton's method , 1986 .

[4]  Stephen M. Robinson,et al.  Normal Maps Induced by Linear Transformations , 1992, Math. Oper. Res..

[5]  Liqun Qi,et al.  A nonsmooth version of Newton's method , 1993, Math. Program..

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

[7]  Liqun Qi,et al.  Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations , 1993, Math. Oper. Res..

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

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

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

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

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

[13]  C. Kanzow,et al.  A Penalized Fischer-Burmeister Ncp-Function: Theoretical Investigation And Numerical Results , 1997 .

[14]  Francisco Facchinei,et al.  A New Merit Function For Nonlinear Complementarity Problems And A Related Algorithm , 1997, SIAM J. Optim..

[15]  Michael C. Ferris,et al.  Complementarity and variational problems : state of the art , 1997 .

[16]  Xiaojun Chen,et al.  Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities , 1998, Math. Comput..

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

[18]  Defeng Sun,et al.  On NCP-Functions , 1999, Comput. Optim. Appl..

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

[20]  Y. Ye,et al.  On Homotopy-Smoothing Methods for Variational Inequalities , 1999 .

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

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

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

[24]  Defeng Sun,et al.  Improving the convergence of non-interior point algorithms for nonlinear complementarity problems , 2000, Math. Comput..

[25]  Song Xu,et al.  The global linear convergence of an infeasible non-interior path-following algorithm for complementarity problems with uniform P-functions , 2000, Math. Program..