Towards the Solution of Large-Scale and Stochastic Traffic Network Design Problems

This thesis investigates the second-best toll pricing and capacity expansion problems when stated as mathematical programs with equilibrium constraints (MPEC). Three main questions are rised: First ...

[1]  M. Patriksson,et al.  Sensitivity analysis of separable traffic equilibrium equilibria with application to bilevel optimization in network design , 2007 .

[2]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2002, SIAM J. Optim..

[3]  A. Shapiro Monte Carlo Sampling Methods , 2003 .

[4]  O. Nelles,et al.  An Introduction to Optimization , 1996, IEEE Antennas and Propagation Magazine.

[5]  Jie Sun,et al.  Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints , 2004, Math. Program..

[6]  Michal Kočvara,et al.  Nonsmooth approach to optimization problems with equilibrium constraints : theory, applications, and numerical results , 1998 .

[7]  Adrian S. Lewis,et al.  A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization , 2005, SIAM J. Optim..

[8]  T. Koopmans,et al.  Studies in the Economics of Transportation. , 1956 .

[9]  Yosef Sheffi,et al.  Urban Transportation Networks: Equilibrium Analysis With Mathematical Programming Methods , 1985 .

[10]  Jeremy G. Siek,et al.  The Boost Graph Library - User Guide and Reference Manual , 2001, C++ in-depth series.

[11]  Jorge Nocedal,et al.  Interior Methods for Mathematical Programs with Complementarity Constraints , 2006, SIAM J. Optim..

[12]  F. Clarke Optimization And Nonsmooth Analysis , 1983 .

[13]  A. V. Levy,et al.  The Tunneling Algorithm for the Global Minimization of Functions , 1985 .

[14]  Donald W. Hearn,et al.  An MPEC approach to second-best toll pricing , 2004, Math. Program..

[15]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[16]  George L. Nemhauser,et al.  Handbooks in operations research and management science , 1989 .

[17]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[18]  D. McFadden Conditional logit analysis of qualitative choice behavior , 1972 .

[19]  Renpu Ge,et al.  A Filled Function Method for Finding a Global Minimizer of a Function of Several Variables , 1990, Math. Program..

[20]  Napsu Karmitsa,et al.  LMBM — FORTRAN Subroutines for Large-Scale Nonsmooth Minimization: User's Manual , 2007 .

[21]  Christodoulos A. Floudas,et al.  Deterministic global optimization - theory, methods and applications , 2010, Nonconvex optimization and its applications.

[22]  Marjo S. Haarala Large-scale nonsmooth optimization : variable metric bundle method with limited memory , 2004 .

[23]  R. Rockafellar,et al.  Optimization of conditional value-at risk , 2000 .

[24]  Philip E. Gill,et al.  Practical optimization , 1981 .

[25]  Sven Leyffer,et al.  Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints , 2006, SIAM J. Optim..

[26]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[27]  Stefan Scholtes,et al.  Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity , 2000, Math. Oper. Res..

[28]  Philip Wolfe,et al.  An algorithm for quadratic programming , 1956 .

[29]  Michael G.H. Bell,et al.  CONTINUOUS EQUILIBRIUM NETWORK DESIGN PROBLEM WITH ELASTIC DEMAND: DERIVATIVE-FREE SOLUTION METHODS , 1998 .

[30]  Yafeng Yin,et al.  Alternative marginal-cost pricing for road networks , 2009 .

[31]  C. Stephens,et al.  Global Optimization Requires Global Information , 1998 .

[32]  P. Zarembka Frontiers in econometrics , 1973 .

[33]  Hillel Bar-Gera,et al.  Traffic Assignment by Paired Alternative Segments , 2010 .