Preprocessing Complementarity Problems
Preprocessing techniques are extensively used in the linear and integer programming communities as a means to improve model formulation by reducing size and complexity. Adaptations and extensions of these methods for use within the complementarity framework are detailed and shown to be effective on practical models. The preprocessor developed is comprised of two phases. The first recasts a complementarity problem as a variational inequality over a polyhedral set and exploits the uncovered structure to fix variables and remove constraints. The second discovers information about the function and utilizes complementarity theory to eliminate variables. The methodology is successfully employed to preprocess several models.
Keywordscomplementarity problems preprocessing variational inequalities
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- A. Brooke, D. Kendrick, and A. Meeraus. GAMS: A User’s Guide. The Scientific Press, South San Francisco, CA, 1988.Google Scholar
- M. C. Ferris, M. P. Mesnier, and J. More. NEOS and Condor: Solving nonlinear optimization problems over the Internet. ACM Transactions on Mathematical Software, forthcoming, 1999.Google Scholar
- M. C. Ferris and T. S. Munson. Case studies in complementarity: Improving model formulation. In M. Thera and R. Tichatschke, editors, Ill-Posed Variational Problems and Regularization Techniques, number 477 in Lecture Notes in Economics and Mathematical Systems, pages 79–98. Springer Verlag, Berlin, 1999.CrossRefGoogle Scholar
- R. Fourer, D. M. Gay, and B. W. Kernighan. AMPL: A Modeling Language for Mathematical Programming. Duxbury Press, 1993.Google Scholar
- D. M. Gay. Electronic mail distribution of linear programming test problems. COAL Newsletter, 13:10–12, 1985.Google Scholar
- ILOG CPLEX Division, 889 Alder Avenue, Incline Village, Nevada. CPLEX Optimizer, http://www.cplex.com
- H. Sellami and S. M. Robinson. Implementation of a continuation method for normal maps. Mathematical Programming, pages 563–578, 1997.Google Scholar