A Comparison of Algorithms for Large Scale Mixed Complementarity Problems

This paper provides a means for comparing various computer codes for solving large scale mixed complementarity problems. We discuss inadequacies in how algorithms are currently compared, and present a testing environment that partially solves these inadequacies. This testing environment consists of library of test problems, along with GAMS and MATLAB interfaces that allow these problems to be easily accessed. Eight different algorithm implementations for large scale mixed complementarity problems are briefly described and tested with default parameter settings using the new testing environment.

[1]  Richaard W. Cottle.  Nonlinear Programs with Positively Bounded Jacobians , 1966 .

[2]  Herbert E. Scarf,et al.  The Approximation of Fixed Points of a Continuous Mapping , 1967 .

[3]  O. Mangasarian.  Equivalence of the Complementarity Problem to a System of Nonlinear Equations , 1976 .

[4]  Stephen M. Robinson,et al.  Generalized Equations , 1982, ISMP.

[5]  W. Rheinboldt,et al.  Pathways to Solutions, Fixed Points, and Equilibria. , 1983 .

[6]  R. Weiner.  Lecture Notes in Economics and Mathematical Systems , 1985 .

[7]  L. Mathiesen.  Computation of economic equilibria by a sequence of linear complementarity problems , 1985 .

[8]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[9]  Patrick T. Harker,et al.  Newton's method for the nonlinear complementarity problem: A B-differentiable equation approach , 1990, Math. Program..

[10]  Jong-Shi Pang,et al.  Newton's Method for B-Differentiable Equations , 1990, Math. Oper. Res..

[11]  Jong-Shi Pang,et al.  Globally Convergent Newton Methods for Nonsmooth Equations , 1992, Math. Oper. Res..

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

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

[14]  Jong-Shi Pang,et al.  NE/SQP: A robust algorithm for the nonlinear complementarity problem , 1993, Math. Program..

[15]  T. Rutherford.  MILES: A Mixed Inequality and nonLinear Equation Solver , 1993 .

[16]  Daniel Ralph,et al.  Global Convergence of Damped Newton's Method for Nonsmooth Equations via the Path Search , 1994, Math. Oper. Res..

[17]  Patrick T. Harker,et al.  A nonsmooth Newton method for variational inequalities, II: Numerical results , 1994, Math. Program..

[18]  Michael C. Ferris,et al.  The GAMS Callable Program Library for Variational and Complementarity Solvers , 1994 .

[19]  Patrick T. Harker,et al.  A nonsmooth Newton method for variational inequalities, I: Theory , 1994, Math. Program..

[20]  T. Rutherford.  Extension of GAMS for complementarity problems arising in applied economic analysis , 1995 .

[21]  M. Ferris,et al.  Projected Gradient Methods for Nonlinear Complementarity Problems via Normal Maps , 1995 .

[22]  João Soares,et al.  Testing a New Class of Algorithms for Nonlinear Complementarity Problems , 1995 .

[23]  S. Dirkse,et al.  Mcplib: a collection of nonlinear mixed complementarity problems , 1995 .

[24]  S. Dirkse,et al.  The path solver: a nommonotone stabilization scheme for mixed complementarity problems , 1995 .

[25]  S. Billups.  Algorithms for complementarity problems and generalized equations , 1996 .

[26]  Andreas Fischer,et al.  On finite termination of an iterative method for linear complementarity problems , 1996, Math. Program..

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

[28]  Francisco Facchinei,et al.  A semismooth equation approach to the solution of nonlinear complementarity problems , 1996, Math. Program..

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

[30]  Jorge J. Moré,et al.  Global Methods for Nonlinear Complementarity Problems , 1994, Math. Oper. Res..

[31]  Michael C. Ferris,et al.  QPCOMP: A quadratic programming based solver for mixed complementarity problems , 1997, Math. Program..

[32]  Michael C. Ferris,et al.  ACCESSING REALISTIC MIXED COMPLEMENTARITY PROBLEMS WITHIN MATLAB , 1996 .

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

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