Nonlinear Programming, Complementarity & Modeling

MA28.1 New AMPL Notation for Complementarity Problems

• David M. Gay; Bell Labs, 600 Mountain Ave., Murray Hill, NJ 07974; dmg@research.bell-labs.com
• Michael C. Ferris; University of Wisconsin, Comp. Sci. Dept., 1210 W Dayton St., Madison, WI 53706; ferris@cs.wisc.edu
• Robert Fourer; Northwestern University, Dept. of IE/MS, Evanston, IL 60208-3119; 4er@iems.nwu.edu

Some problems involve complementarity constraints: pairs of inequalities, at least one of which must be tight. New, flexible AMPL syntax provides a convenient way to state such constraints, which are turned into a canonical form for solvers. This extends AMPL to (non)linear complementarity problems and optimization problems with equilibrium constraints.

MA28.2 Solution Environments for MPEC & NLP Models

• Steven P. Dirkse; GAMS Development Corp., 1217 Potomac St. NW, Washington, DC 20007; steve@gams.com

We have developed a machine-independent interface to the GAMS MPEC model that allows access from within MATLAB, and have generalized this to other classes of models, i.e., CNS, NLP, LP, etc., and to other computational environments. This provides a wealth of source problems for the algorithm developer and visualization/analysis tools for the modeler.

MA28.3 Combining Nonlinear Programming & Nonlinear Complementarity Solvers

• Arne Stolbjerg Drud; ARKI Consulting & Development, A/S, 246 A, Bagsvaerd, DK-2880 , Denmark; adrud@arki.dk

A model defined in GAMS belongs to a model class such as NLP or MCP. However, some NLP models are better solved as MCP and vice versa. We explore the translation of models from one class to another and report on performance on practical models.

MA28.4 A Predictor-Corrector Method for Nonlinear Complementarity Problems

• Danny Ralph; University of Melbourne, Dept. of Math. & Stats., Parkville, Vic, 3052 , Australia; danny@mundoe.maths.mu.oz.au
• Michael C. Ferris; University of Wisconsin, Comp. Sci. Dept., 1210 W Dayton St., Madison, WI 53706; ferris@cs.wisc.edu

NCPs are often solved as nondifferentiable equations. We investigate a class of algorithms for solving equations called homotopy or continuation methods. Specifically, we look at a piecewise smooth formulation of NCPs called the normal equation and apply a predictor-corrector method that uses piecewise linear subproblems.