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Complementarity Problems

The linear complementarity problem is applied for the development of theory and algorithms in linear programming, and in quadratic programming. Nonlinear complementarity problems have been applied to the solution of Nash equilibrium, traffic assignment or network equilibrium, spatial price equilibrium and the general or Walrasian equilibrium problems.

A large collection of complementarity test problems, reffered as the Mixed Complementarity Problems LIBrary, MCPLIB, is publicly available via anonymous ftp from ftp://ftp.cs.wisc.edu/pub/mcplib/ and are presented in GAMS modeling language.

The standard GAMS distribution includes a library of test problems that is also available from http://www.gams.com/modlib/modlib.htm.

Both collections contain problems with known types of computational difficulties or real life applications. Selected test problems from both libraries are included below.

Linear Complementarity Problems

Test Problem Description Gams File
1 MCPLIB ex10.1.1.gms
2 Cottle-et.al., (1992)-I ex10.1.2.gms
3 Cottle-et.al., (1992)-II ex10.1.3.gms
4 Cottle-et.al., (1992)-Bimatrix Game ex10.1.4.gms
5 Dantzig's equilibrium transportation model ex10.1.5.gms
6 Cottle-et.al., (1992)-III ex10.1.6.gms

Nonlinear Complementarity Problems

Test Problem Description Gams File
1 MCPLIB-I ex10.2.1.gms
2 Dirkse-Ferris (1995) ex10.2.2.gms
3 Walrasian equilibrium model ex10.2.3.gms
4 Nash equilibrium of a 5-firm noncooperative game ex10.2.4.gms
5 Cournot-Nash equilibrium problem with 10 firms ex10.2.5.gms
6 Invariant Capital Stock Problem ex10.2.6.gms

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