Models and applications of optimal transport in economics, traffic, and urban planning

Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into account traffic congestion effects is the first topic, and it shows various links with Monge-Kantorovich theory and PDEs. Then, two models for urban planning are introduced. The last section is devoted to two problems from economics and their translation in the language of optimal transport.

[1]  Giuseppe M. Buttazzo,et al.  A Mass Transportation Model for the Optimal Planning of an Urban Region , 2009, SIAM Rev..

[2]  J. Morel,et al.  Optimal Transportation Networks: Models and Theory , 2008 .

[3]  Régularité des solutions d'un problème variationnel sous contrainte de convexité , 2001 .

[4]  Luigi De Pascale,et al.  Sharp summability for Monge Transport density via Interpolation , 2004 .

[5]  Filippo Santambrogio,et al.  Introduction to optimal transport theory , 2010, Optimal Transport.

[6]  G. Carlier,et al.  Equilibrium structure of a bidimensional asymmetric city , 2007 .

[7]  Y. Brenier.  Polar Factorization and Monotone Rearrangement of Vector-Valued Functions , 1991 .

[8]  Giuseppe M. Buttazzo,et al.  A Model for the Optimal Planning of an Urban Area , 2005, SIAM J. Math. Anal..

[9]  Guillaume Carlier,et al.  Congested traffic dynamics, weak flows and very degenerate elliptic equations , 2010 .

[10]  Filippo Santambrogio.  Absolute continuity and summability of transport densities: simpler proofs and new estimates , 2009 .

[11]  Filippo Santambrogio.  Variational Problems in Transport Theory with Mass Concentration , 2008 .

[12]  J. Rochet,et al.  Ironing, Sweeping, and Multidimensional Screening , 1998 .

[13]  Guillaume Carlier,et al.  Optimal Transportation with Traffic Congestion and Wardrop Equilibria , 2006, SIAM J. Control. Optim..

[14]  H. Hotelling.  Stability in Competition , 1929 .

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

[16]  Integral Estimates for Transport Densities , 2004 .

[17]  L. Evans,et al.  Differential equations methods for the Monge-Kantorovich mass transfer problem , 1999 .

[18]  John R. Beaumont,et al.  Spatial Economics: Density, Potential and Flow , 1986 .

[19]  G. Carlier,et al.  A variational model for urban planning with traffic congestion , 2005 .

[20]  G. Carlier,et al.  The Structure of Cities , 2004, J. Glob. Optim..

[21]  P. Lions,et al.  Mean field games , 2007 .

[22]  T. Raa.  Spatial economics: density, potential, and flow: Martin BECKMANN and Tönu PUU Volume 14 in: Studies in Regional Science and Urban Economics, North-Holland, Amsterdam, 1985, xii + 276 pages, Dfl. 125.00 , 1986 .

[23]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[24]  A. Pratelli,et al.  Regularity properties for Monge transport density and for solutions of some shape optimization problem , 2002 .

[25]  Guy Bouchitté,et al.  New lower semicontinuity results for nonconvex functionals defined on measures , 1990 .

[26]  M. Beckmann.  A Continuous Model of Transportation , 1952 .

[27]  Filippo Santambrogio.  Transport and concentration problems with interaction effects , 2007, J. Glob. Optim..

[28]  Giuseppe Buttazzo.  Three Optimization Problems in Mass Transportation Theory , 2006 .