Abstract
We describe several new tools for modeling MPEC problems that are built around the introduction of an MPEC model type into the GAMS language. We develop subroutines that allow such models to be communicated directly to MPEC solvers. This library of interface routines, written in the C language, provides algorithmic developers with access to relevant problem data, including for example, function and Jacobian evaluations. A MATLAB interface to the GAMS MPEC model type has been designed using the interface routines. Existing MPEC models from the literature have been written in GAMS, and computational results are given that were obtained using all the tools described.
This material is based on research supported by National Science Foundation Grant CCR9619765.
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References
A. Bachem, M. Grötchel, and B. Korte, editors. Mathematical Programming: The State of the Art, Bonn 1982, Berlin, 1983. Springer Verlag.
J. F. Bard. Convex two-level optimization. Mathematical Programming, 40: 15–27, 1988.
J. Bisschop and R. Entriken. AIMMS - The Modeling System. Paragon Decision Technology, Haarlem, The Netherlands, 1993.
A. Brooke, D. Kendrick, and A. Meeraus. GAMS: A User’s Guide. The Scientific Press, South San Francisco, CA, 1988.
A. H. DeSilva. Sensitivity Formulas for Nonlinear Factorable Programming and their Application to the Solution of an Implicitly Defined Optimization Model of US Crude Oil Production. PhD thesis, George Washington University, Washington, D.C., 1978.
S. P. Dirkse and M. C. Ferris. MCPLIB: A collection of nonlinear mixed complementarity problems. Optimization Methods and Software, 5: 319345, 1995.
S. P. Dirkse and M. C. Ferris. The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems. Optimization Methods and Software, 5: 123–156, 1995.
S. P. Dirkse and M. C. Ferris. A pathsearch damped Newton method for computing general equilibria. Annals of Operations Research, 1996.
S. P. Dirkse and M. C. Ferris. Traffic modeling and variational inequalities using GAMS. In Ph. L. Toint, M. Labbe, K. Tanczos, and G. Laporte, editors, Operations Research and Decision Aid Methodologies in Traffic and Transportation Management, NATO ASI Series F. Springer-Verlag, 1997.
S. P. Dirkse, M. C. Ferris, P. V. Preckel, and T. Rutherford. The GAMS callable program library for variational and complementarity solvers. Mathematical Programming Technical Report 94–07, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, 1994.
F. Facchinei, H. Jiang, and L. Qi. A smoothing method for mathematical programs with equilibrium constraints. Technical report, Universitâ di Roma “La Sapienza”, Roma, Italy, 1996.
M. C. Ferris, R. Fourer, and D. M. Gay. Expressing complementarity problems and communicating them to solvers. Mathematical Programming Technical Report 98–02, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, 1998.
M. C. Ferris and T. F. Rutherford. Accessing realistic complementarity problems within Matlab. In G. Di Pillo and F. Giannessi, editors, Nonlinear Optimization and Applications, pages 141–153. Plenum Press, New York, 1996.
R. Fourer, D. Gay, and B. Kernighan. AMPL. The Scientific Press, South San Francisco, California, 1993.
M. Fukushima, Z.-Q. Luo, and J. S. Pang. A globally convergent sequential quadratic programming algorithm for mathematical programs with linear complementarity constraints. Computational Optimization and Applications, forthcoming, 1997.
P. T. Harker. Generalized Nash games and quasi-variational inequalities. European Journal of Operations Research, 54: 81–94, 1987.
P. T. Harker and J. S. Pang. Finite—dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming, 48: 161–220, 1990.
J. M. Henderson and R. E. Quandt. Microeconomic Theory. McGraw—Hill, New York, 3rd edition, 1980.
H. Jiang and D. Ralph. QPECgen, a matlab generator for mathematical programs with quadratic objectives and affine variational inequality constraints. Technical report, The University of Melbourne, Department of Mathematics and Statistics, Parkville, Victoria, Australia, 1997.
M. Kocvara and J. V. Outrata. On optimization of systems governed by implicit complementarity problems. Numerical Fucntional Analysis and Optimization, 15: 869–887, 1994.
M. Kocvara and J. V. Outrata. On the solution of optimum design problems with variational inequalities. In Recent Advances in Nonsmooth Optimization, pages 172–192. World Scientific Publishers, Singapore, 1995.
A. Kuntsevich and F. Kappel. SolvOpt: The solver for local nonlinear optimization problems. Institute for Mathematics, Karl-Franzens University of Graz, 1997.
Z.-Q. Luo, J. S. Pang, and D. Ralph. Mathematical Programs with Equilibrium Constraints. Cambridge University Press, 1996.
Frederic H. Murphy, Hanif D. Sherali, and Allen L. Soyster. A mathematical programming approach for determining oligopolistic market equilibrium. Mathematical Programming, 24: 92–106, 1982.
J. V. Outrata. On optimization problems with variational inequality constraints. SIAM Journal on Optimization, 4: 340–357, 1994.
J. V. Outrata and J. Zowe. A numerical approach to optimization problems with variational inequality constraints. Mathematical Programming, 68: 105–130, 1995.
D. Ralph. A piecewise sequential quadratic programming method for mathematical programs with linear complementarity constraints. In Proceedings of the Seventh Conference on Computational Techniques and Applications (CTAC95), 1996.
R. Raman. Integration of logic and heuristic knowledge in discrete optimization techniques for process systems. PhD thesis, Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania, 1993.
S. M. Robinson. Strongly regular generalized equations. Mathematics of Operations Research 5:43–62 1980.
S. M. Robinson. Generalized equations. In Bachem et al. [1], pages 346367.
H. Schramm and J. Zowe. A version of the bundle idea for minimizing a nonsmooth function: Conceptual idea, convergence analysis, numerical results. SIAM Journal on Optimization, 2:121–152, 1992.
N. Z. Shor. Minimization Methods for Nondifferentiable Functions. Springer-Verlag, Berlin 1985.
H. Van Stackelberg. The Theory of Market Economy. Oxford University Press 1952.
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Dirkse, S.P., Ferris, M.C. (1998). Modeling and Solution Environments for MPEC: GAMS & MATLAB. In: Fukushima, M., Qi, L. (eds) Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods. Applied Optimization, vol 22. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6388-1_7
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