Solution Of The Urban Traffic Problem With Fixed Demand Using Inexact Restoration

Congested traffic has become a part of the day-to-day for the residents of big metropolitan centers. From an economic viewpoint, this problem has been causing huge financial damage and strategic measures must be taken to tackle it. An alternative means of solving the problem is the inclusion of toll charges on routes with a view to decongesting the road network. The mathematical formulation of this alternative involves the solving of an optimization problem with equilibrium constraints (MPEC). This work proposes an algorithm for the solution of this problem based on the strategy of inexact restoration.837-4019071918Andreani, R., Castro, S.L.C., Chela, J.L., Friedlander, A., Santos, S.A., Aninexact-restoration method for nonlinear bilevel programming problems (2009) Comput. Optim. Appl., 43, pp. 307-328Andreani, R., Martinez, J.M., Svaiter, B.F., On the Regularization of mixed complementarity problems (2000) Numerical Functional Analysis and Optimization, 21, pp. 589-600Andreani, R., Martinez, J.M., On the reformulation od Nonlinear Complementarity Problems using the Fischer-Burmeister function (1999) Applied Mathematics Letters, 12, pp. 7-12Andreani, R., Friedlander, A., Bound Constrained Smooth Optimization for Solving Variational Inequalities and Related Problems (2002) Annals of Operations Research, 116, pp. 179-198Arnott, R., Small, K., (1994) The economics of traffic congestion, , Boston College Working Papers in Economics 256, Boston College, Department of EconomicsBazarra, M.S., Sherali, H.D., Shetty, C.M., (1993) Nonlinear Programming: Theory and Algoritms, , Second Edition, John Wiley & Sons, New YorkBonnans, J.F., Shapiro, A., (2000) Perturbation Analysis of Optimization Problems, , Springer Series in Operations Research, SpringerBrotcorne, L., Labbé, M., Marcotte, P., Savard, G., A Bilevel Model for Toll Optimization on a Multicommodity Transportation Network (2001) Transportation Science, 35 (4), pp. 345-358Calamai, P.H., Vicente, L.N., Generating quadratic bilevel programming test problems (1994) ACM Transactions on Mathematical Software, 20, pp. 103-119Chela, J.L., (2006) Resolução do problem a de programao matemática com restrições de equilíbrio usando restauração inexata, , PhD thesis, University of CampinasFerrari, P., Road network toll pricing and social welfare (2002) Trans. Res. B, 36, pp. 471-483Harker, P.T., Pang, J.S., Existence of optimal solutions to mathematical programs with equilibrium constraints (1988) Operations Research Letters, 7 (2), pp. 61-64Hearn, D.W., (1980) Bounding Flows in Traffic Assignment Models, , Research report N.80-4, Dept. of Industrial and Systems Enginnering, University of Florida, Gainesville, FL 32611Hearn, D.W., Ramana, M.V., Solving congestion toll princing models (1998) Equilibrium and Advanced Transportation Modelling, pp. 109-124. , P. Marcotte, S. Nguyen (eds), Kluwer Academic Publisher, Boston, The NetherlandsHearn, D.W., Yildirim, M.B., A toll pricing framework for traffic assignment problems with elastic demands (2001) Current Trends in Transportation and Network Analysis: Miscellanea in Honor of Michael Florian, , M. Gendreau, P. Marcotte(eds), Kluwer Academic Publisher, Dordrecht, The NetherlandsHearn, D.W., Lawphongpanich, S., An MPEC approach to second-best toll pricing (2004) Mathematical Programming Series B, 101, pp. 33-55Hearn, D.W., Bergendorff, P., Ramana, M.V., Congestion Toll Pricing of Traffic Networks, Network Optimization (1997) Lecture Notes in Economics and Mathematical Systems, 450, pp. 51-71. , P. M. Pardalos, D.W. Hearn and W.W. Hager (Eds.), Springer-VerlagJohansson-Stenman, O., Sterner, T., What is the scope for environmental road pricing? (1998) Road pricing Traffic Congestion and Environment, , K.J. Button, E.T. Verhoef (eds.), Edward Elgar Publishing Limited, London, EnglandLabbé, M., Marcotte, P., Savard, G., A bilevel model of taxation and its application to optimal highway pricing (1998) Manage. Sci, 44 (12), pp. 1608-1622Migdalas, A., Bilevel Programming in traffic planning: models, methods and challenge (1994) Journal of Global Optimization, 4, pp. 340-357Patriksson, M., Rockafellar, R.T., A Mathematical model and descent algorithm for bilevel traffic management (2002) Trans. Sci, 36, pp. 271-291Solodov, M.V., Svaiter, B.F., A New Projection Method for Variational Inequality Problems (1999) SIAM Journal Control Optimization, 37, pp. 765-77

Bound constrained smooth optimization for solving variational inequalities and related problems

Variational inequalities and related problems may be solved via smooth bound constrained optimization. A comprehensive discussion of the important features involved with this strategy is presented. Complementarity problems and mathematical programming problems with equilibrium constraints are included in this report. Numerical experiments are commented. Conclusions and directions of future research are indicated