Solving Stochastic Mathematical Programs with Complementarity Constraints Using Simulation
Published Online:1 Nov 2006https://doi.org/10.1287/moor.1060.0215
References
- Practical Bilevel Optimization (1998) (Kluwer Academic Publishers, Dordrecht, The Netherlands) Crossref, Google Scholar
- Simulation-based solution of stochastic mathematical programs with complementarity constraints: Sample-path analysis. (2004) . CentER discussion paper, ISSN: 0924-7815, Tilburg University, Tilburg, The Netherlands. Available at http://greywww.kub.nl:2080/greyfiles/center/2004/doc/25.pdfGoogle Scholar
- , Ingalls R. G., Rossetti M. D., Smith J. S., Peters B. A. Solving stochastic mathematical programs with complementarity constraints using simulation. Proc. 2004 Winter Simulation Conf., Washington, D.C. (2004) (IEEE, Piscataway, NJ) 550–558Crossref, Google Scholar
- Bureau of Public RoadsTraffic Assignment Manual (1964) . U.S. Department of Commerce, Urban Planning Division, Washington, D.C.Google Scholar
- Foundations of Bilevel Programming (2002) (Kluwer Academic Publishers, Dordrecht, The Netherlands) Google Scholar
- , Toint Ph. L., Labbe M., Tanczos K., Laporte G. Traffic modeling and variational inequalities using GAMS. Operations Research and Decision Aid Methodologies in Traffic and Transportation Management. (1998) 6(Springer-Verlag)136–163NATO ASI Series FCrossref, Google Scholar
- CONOPT: A GRG code for large sparse dynamic nonlinear optimization problems. Math. Programming (1985) 31:153–191Crossref, Google Scholar
- Finite-Dimensional Variational Inequalities and Complementarity Problems (2003) (Springer-Verlag, New York) Google Scholar
- , Kehoe T. J., Srinivasan T. N., Whalley J. Mathematical programs with equilibrium constraints: Automatic reformulation and solution via constrained optimization. Frontiers in Applied General Equilibrium Modeling (2005) (Cambridge University Press, Cambridge, UK) 67–93Available at http://web.comlab.ox.ac.uk/oucl/publications/natr/na–02–11.htmlCrossref, Google Scholar
- Engineering and economic applications of complementarity problems. SIAM Rev. (1997) 39:669–713Crossref, Google Scholar
- , Ball M. O., Magnanti T., Monma C., Nemhauser G. Network equilibrium models and algorithms. Network Routing Handbooks in OR and MS (1995) 8(Elsevier Science, Amsterdam, The Netherlands) 485–550Crossref, Google Scholar
- Gradient Estimation via Perturbation Analysis (1991) (Kluwer, Norwell, MA) Google Scholar
- Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation (2000) (SIAM, Philadelphia, PA) Google Scholar
- , Charnes J. M., Morrice D. M., Brunner D. M., Swain J. J. Sample-path solution of stochastic variational inequalities, with applications to option pricing. Proc. 1996 Winter Simulation Conf., Coronado, CA (1996) (IEEE, Piscataway, NJ) 337–344Crossref, Google Scholar
- Sample-path solution of stochastic variational inequalities. Math. Programming (1999) 84:313–333Crossref, Google Scholar
- , Sturrock D. T., Farrington P. A., Nembhard H. B., Evans G. W. Solving stochastic optimization problems with stochastic constraints: An application in network design. Proc. 1999 Winter Simulation Conf., Phoenix, AZ (1999) (IEEE, Piscataway, NJ) 471–478Crossref, Google Scholar
- Perturbation Analysis of Discrete Event Dynamical Systems (1991) (Kluwer, Norwell, MA) Crossref, Google Scholar
- Approximation to optimization problems: An elementary review. Math. Oper. Res. (1986) 11:9–18Link, Google Scholar
- The sample average approximation method for stochastic discrete optimization. SIAM J. Optim. (2001) 12:479–502Crossref, Google Scholar
- , Robinson S. M. Strongly stable stationary solutions in nonlinear programming. Analysis and Computation of Fixed Points (1980) (Academic Press, New York) 93–138Crossref, Google Scholar
- An MPEC approach to second-best toll pricing. Math. Programming (2004) 101:33–55Crossref, Google Scholar
- Smoothing implicit programming approaches for stochastic mathematical programs with linear complementarity constraints. (2003) . Technical report 2003-006, Department of Applied Mathematics and Physics, Kyoto University, Kyoto, JapanGoogle Scholar
- The empirical behavior of sampling methods for stochastic programming. (2002) . Optimization technical report 02-01, Computer Sciences Department, University of Wisconsin-Madison, Madison, WI. Available at http://www.cs.wisc.edu/∼swright/papers/uwopt-0201.pdfGoogle Scholar
- Mathematical Programs with Equilibrium Constraints (1996) (Cambridge University Press, Cambridge, UK) Crossref, Google Scholar
- Topology: A First Course (1975) (Prentice Hall, Englewood Cliffs, NJ) Google Scholar
- Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory, Applications and Numerical Results (1998) (Kluwer Academic Publishers, Boston, MA) Crossref, Google Scholar
- Stochastic mathematical programs with equilibrium constraints. Oper. Res. Lett. (1999) 25:159–167Crossref, Google Scholar
- , Schoen J. Throughput optimization in tandem production lines via nonsmooth programming. Proc. 1993 Summer Computer Simulation Conf. (1993) (Society for Computer Simulation, San Diego, CA) 70–75Google Scholar
- Sample-path optimization of convex stochastic performance functions. Math. Programming (1996) 137–176Crossref, Google Scholar
- Generalized equations and their solutions, Part I: Basic theory. Math. Programming Study (1979) 10:128–141Crossref, Google Scholar
- Strongly regular generalized equations. Math. Oper. Res. (1980) 5:43–62Link, Google Scholar
- Analysis of sample-path optimization. Math. Oper. Res. (1996) 21:513–528Link, Google Scholar
- Variational Analysis (1998) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
- Discrete event systems: Sensitivity analysis and stochastic optimization by the score function method (1993) (Wiley, Chichester, UK) Google Scholar
- Ein Straffunktionsansatz für Optimierungsprobleme mit Gleichgewichtsrestriktionen. (1995) . Diploma thesis, Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Karlsruhe, GermanyGoogle Scholar
- Mathematical programs with complementarity constraints: Stationarity, optimality and sensitivity. Math. Oper. Res. (2000) 25:1–22Link, Google Scholar
- Introduction to piecewise differentiable equations. (1994) . Habilitation thesis, Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Karlsruhe, GermanyGoogle Scholar
- Stochastic programming with equilibrium constraints. (2004) . Technical report, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA. Available at Optim. Online http://www.optimization-online.org/DB_HTML/2004/08/930.htmlGoogle Scholar
- A simulation-based approach to two-stage stochastic programming with recourse. Math. Programming (1998) 81:301–325Crossref, Google Scholar
- Generalized semi-infinite programming: Theory and methods. Eur. J. Oper. Res. (1999) 119:301–303Crossref, Google Scholar
- Transportation Research BoardHighway Capacity Manual (2000) . Washington, D.C.Google Scholar
- Some theoretical aspects of road traffic research. Proc. Institution Civil Engineers (1952) 2:325–378Crossref, Google Scholar
- , Pardalos P., Floudas C. Stochastic bilevel programs. Encyclopedia of Optimization (2001) (Kluwer Academic Publishers, Dordrecht, The Netherlands) Crossref, Google Scholar
- Sensitivity analysis for stochastic user equilibrium network flows—a dual approach. Transportation Sci. (2001) 35:124–133Link, Google Scholar
- Modeling variable demand equilibrium under second-best road pricing. Transportation Res. B (1997) 38(4):733–749Google Scholar

