Sensitivity Analysis of Aggregated Variational Inequality Problems, with Application to Traffic Equilibria

References

• Cho H.-J., Smith T. E., Friesz T. L. A reduction method for local sensitivity analyses of network equilibrium arc flows. Transportation Res. (2001) 34B:31–51Google Scholar
• Codina E., BarcelÓ J. Adjustment of O-D trip matrices from observed volumes: An algorithmic approach based on conjugate directions. (2000) . Report, Statistics and Operations Research Department, Polytechnic University of Catalonia, Barcelona, SpainGoogle Scholar
• Dontchev A. L., Rockafellar R. T. Ample parameterization of variational inclusions. SIAM J. Optim. (2002) 12:170–187Crossref, Google Scholar
• Drissi-Kaïtouni O., Lundgren J. T. Bilevel origin-destination matrix estimation using a descent approach. (1992) . Report LiTHMAT-R-1992-49, Department of Mathematics, Linköping Institute of Technology, Linköping, SwedenGoogle Scholar
• Friesz T. L., Tobin R. L., Cho H. J., Mehta N. J. Sensitivity analysis-based heuristic algorithms for mathematical programs with variational inequality constraints. Math. Programming (1990) 48:265–284Crossref, Google Scholar
• Larsson T., Lundgren J., Patriksson M., Rydergren C., Giannessi F., Maugeri A., Pardalos P. M. Most likely traffic equilibrium route flows: Analysis and computation. Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models (2001) (Kluwer Academic Publishers, Dordrecht The Netherlands) 129–159Google Scholar
• Luo Z.-Q., Pang J.-S., Ralph D.Mathematical Programs with Equilibrium Constraints (1996) (Cambridge University Press, Cambridge, U.K) Crossref, Google Scholar
• Mifflin R. Semismooth and semiconvex functions in constrained optimization. SIAM J. Control and Optim. (1977) 15:959–972Crossref, Google Scholar
• Nagurney A.Network Economics: A Variational Inequality Approach (2000) 2nd ed(Kluwer Academic Publishers, Dordrecht The Netherlands) Google Scholar
• Outrata J. V., Gritzmann P., Horst R., Sachs E., Tichatschke R. On a special class of mathematical programs with equilibrium constraints. Recent Advances in Optimization. Lecture Notes in Economics and Mathematical Systems (1997) 452(Springer-Verlag, Berlin, Germany) 246–260Crossref, Google Scholar
• Outrata J. V., Kočvara M., Zowe J.Nonsmooth Approach to Optimization Problems with Equilibrium Constraints (1998) (Kluwer Academic Publishers, Dordrecht, The Netherlands) Crossref, Google Scholar
• Patriksson M.The Traffic Assignment Problem—Models and Methods. Topics in Transportation (1994) (VSP BV, Utrecht, The Netherlands) Google Scholar
• Patriksson M. Sensitivity analysis of traffic equilibria. (2001) . Report, Department of Mathematics, Chalmers University of Technology, Gothenburg, Sweden. Revised 2002 for Transportation Sci.Google Scholar
• Patriksson M., Rockafellar R. T. A mathematical model and descent algorithm for bilevel traffic management. Transportation Sci. (2002) 36:271–291Link, Google Scholar
• Qiu Y., Magnanti T. L. Sensitivity analysis for variational inequalities defined on polyhedral sets. Math. Oper. Res. (1989) 14:410–432Link, Google Scholar
• Robinson S. M. Strongly regular generalized equations. Math. Oper. Res. (1980) 5:43–62Link, Google Scholar
• Rockafellar R. T., Wets R.J.-B.Variational Analysis—Grundlehren der mathematischen Wissenschaften (1998) 317(Springer-Verlag, Berlin, Germany) Google Scholar
• Spiess H. A gradient approach for the O-D matrix adjustment problem. (1990) . Publication CRT-693, Centre de recherche sur les transports, Université de Montréal, Montréal, Quebec, CanadaGoogle Scholar
• Tobin R. L., Friesz T. L. Sensitivity analysis for equilibrium network flow. Transportation Sci. (1988) 22:242–250Link, Google Scholar
• Yang H. Heuristic algorithms for the bilevel origindestination matrix estimation problems. Transportation Res. (1995) 29B:231–242Crossref, Google Scholar
• Yang H., Bell M. G. H. Traffic restraint, road pricing and network equilibrium. Transportation Res. (1997) 31B:303–314Crossref, Google Scholar
• Yen N. D. Lipschitz continuity of solutions of variational inequalities with a parametric polyhedral constraint. Math. Oper. Res. (1995) 20:695–708Link, Google Scholar