Numerical Approach of Network Problems in Optimal Mass Transportation

Show more

References

[1] A. Figalli, “Optimal Transportation and Action-Minimizing Measures,” Ph.D. Thesis, Scuola Normale Superiore, Pisa, 2007.

[2] G. Buttazzo, E. Oudet and E. Stepanov, “Optimal Transportation Problems with Free Dirichlet Regions,” Progress in Non-Linear Differential Equations, Vol. 51, 2002, pp. 41-65.

[3] G. Buttazzo, A. Pratelli, S. Solimini and E. Stepanov, “Optimal Urbain Networks via Mass Transportation,” Lecture Notes in Mathematics, Vol. 1961, 2009, pp. 75103.

[4] G. Buttazzo, “Three Optimization Problems in Mass Transportation Theory,” Nonsmooth Mechanics and Analysis, Vol. 12, 2006, pp. 13-23.

[5] E. Oudet, “Some Results in Shape Optimization and Optimization,” 2002.
http://www-ljk.imag.fr/membres/Edouard.Oudet/index.php?page=cv/node2

[6] L. Ambrosio, “Mathematical Aspects of Evolving Interfaces,” Lectures Notes in Mathematics, Vol. 1812, 2003, pp. 1-52.

[7] L. Ambrosio and P. Tilli, “Select Topics on ‘Analysis on Metric Espaces’,” Appunti dei Corsi Tenuti da Docenti delle Scuola, Scuola Normale superiore, Pisa, 2000.

[8] L. Caffarelli, M. Feldman and R. J. McCann, “Constructing Optimal Maps for Monge’s Transport Problem as a Limit of Strictly Convex Costs,” Journal of the American Mathematical Society, Vol. 15, No. 1, 2002, pp. 1-26.
doi:10.1090/S0894-0347-01-00376-9

[9] L. C. Evans and W. Gangbo, “Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem,” Memoirs of the American Mathematical Society, Vol. 137, No. 653, 1999, pp. 1-66.

[10] A. Pratelli, “Existence of Optimal Transport Maps and Regularity of the Transport Density in Masse Transportation Problems,” Ph.D. Thesis, Scuola Normale Superiore, Pisa, 2003. http://cvgmt.sns.it/

[11] C. Villani, “Topics in Optimal Transportation,” Graduate Studies in Mathematics, Vol. 58, 2003.

[12] C. Villani, “Optimal Transport, Old and New,” Springer, Berlin, 2008.

[13] V. N. Sudakov, “Geometric Problems in the Theory of Infinite Dimensional Distributions,” Proceedings of the Steklov Institute of Mathematics, Vol. 141, 1976, pp. 1178.

[14] Y. Brenier, “Optimal Transportation and Applications,” Extended Monge-Kantorovich Theory,” Lecture Notes in Mathematics, Vol. 1813, 2003, pp. 91-121.

[15] G. Carlier, C. Jimenez and F. Santambrogio, “Optimal Transportation with Traffic Congestion and Wardrop Equilibria,” CVGMT Prepint, 2006. http://cvgmt.sns.it

[16] G. Buttazzo, C. Jimenez and E. Oudet, “An Optimization Problem for Mass Transportation with Congested Dynamics,” SIAM Journal on Control and Optimization, Vol. 48, No. 3, 2009.

[17] F. Santambrogio, “Variational Problems in Transport Theory with Mass Concentration,” Ph.D. Thesis, Scuola Normale Superiore, 2006.

[18] A. Brancolini and G. Buttazzo, “Optimal Networks for Mass Transportation Problems,” Preprint Diparttimento di Matematica Universit di Pisa, Pisa, 2003.

[19] G. Buttazzo and E. Stepanov, “Optimal Transportation Networks as Free Dirichlet Regions for the Monge-Kantorovich Problem,” Annali della Scuola Normale Superiore di Pisa—Classe di Scienze, Vol. 2, No. 4, 2003, pp. 631-678.

[20] C. B. Djiba, “Optimal Assignment of Routes to a Terminal for an Urban Transport Network,” Master of Research Engineering Sciences, Cheikh Anta Diop University, ESP Dakar, 2008.

[21] Dakar Dem Dikk, Full Traffic 2008-2009, File InputOutput, 2008. http://www.demdikk.com

[22] INRO Consultants Inc., “EMME User’s Manual,” 2007.

[23] A. W?chter and L. T. Biegler, “Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence,” SIAM Journal on Optimization, Vol. 16, No. 1, 2005, pp. 1-31. doi:10.1137/S1052623403426556

[24] A. W?chter and L. T. Biegler, “On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming,” Mathematical Programming, Vol. 106, No. 1, 2006, pp. 25-57.
doi:10.1007/s10107-004-0559-y

[25] R. Fourer, D. M. Gay and B. W. Kernighan, “AMPL: A Modeling Language For Mathematical Programming,” Thomson Publishing Company, Danvers, 1993.