Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Multi-marginal optimal transport and multi-agent matching problems: Uniqueness and structure of solutions
Pages: 1623 - 1639, Issue 4, April 2014

doi:10.3934/dcds.2014.34.1623      Abstract        References        Full text (413.9K)           Related Articles

Brendan Pass - Department of Mathematical and Statistical Sciences, 632 CAB, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1, Canada (email)

1 M. Agueh and G. Carlier, Barycenters in the Wasserstein space, SIAM J. Math. Anal., 43 (2011), 904-924.       
2 M. Beiglbock, P. Henry-Labordere and F. Penkner, Model independent bounds for option prices: A mass transport approach, Finance Stoch., 17 (2013), 477-501.
3 M. Bernot, J. Delon, G. Peyre and J. Rabin, Wasserstein barycenter and its application to texture mixing, in "Scale Space and Variational Methods in Computer Vision," (eds A. Bruckstein, B. Haar Romeny, A. Bronstein, and M. Bronstein), 435-446, Lecture Notes in Computer Science, 6667, Springer, Berlin, 2012.
4 Y. Brenier, Décomposition polaire et réarrangement monotone des champs de vecteurs, (French) [Polar decomposition and increasing rearrangement of vector fields] C. R. Acad. Sci. Pair. Ser. I Math., 305 (1987), 805-808.       
5 Y. Brenier, Extended Monge-Kantorovich theory, in "Optimal Transportation and Applications," (Martina Franca, 2001), 91-121, Lecture Notes in Math., 1813, Springer, Berlin, 2003.       
6 G. Buttazzo, L. De Pascale and P. Gori-Giorgi, Optimal-transport formulation of electronic density-functional theory, Phys. Rev. A, 85 (2012), 062502.
7 L. Caffarelli, Allocation maps with general cost functions, in "Partial Differential Equations and Applications" (eds P. Marcellini, G. Talenti and E. Vesintini), Dekker, (1996), 29-35.       
8 G. Carlier, On a class of multidimensional optimal transportation problems, J. Convex Anal., 10 (2003), 517-529.       
9 G. Carlier and I. Ekeland, Matching for teams, Econom. Theory, 42 (2010), 397-418.       
10 G. Carlier and B.Nazaret, Optimal transportation for the determinant, ESAIM Control, Optim. Calc. Var., 14 (2008), 678-698.       
11 P-A. Chiapporri, R. McCann and L. Nesheim, Hedonic price equilibria, stable matching and optimal transport: Equivalence, topology and uniqueness, Econom. Theory, 42 (2010), 317-354.       
12 C. Cotar, G. Friesecke and C. Klüppelberg, Density functional theory and optimal transportation with Coulomb cost, Comm. Pure Appl. Math., 66 (2013), 548-599.       
13 I. Ekeland, An optimal matching problem, ESAIM Control, Optim. Calc. Var., 11 (2005), 57-71(electronic).       
14 A. Galichon and N. Ghoussoub, Variational representations for N-cyclically monotone vector fields, preprint, arXiv:1207.2408.
15 A. Galichon and P. Henry-Labordere and N. Touzi, A stochastic control approach to non-arbitrage bounds given marginals, with an application to Lookback options, Preprint available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1912477.
16 W. Gangbo and R. McCann, The geometry of optimal transportation, Acta Math., 177 (1996), 113-161.       
17 W. Gangbo and A. Święch, Optimal maps for the multidimensional Monge-Kantorovich problem, Comm. Pure Appl. Math., 51 (1998), 23-45.       
18 N. Ghoussoub and A. Moameni, Symmetric Monge Kantorovich problems and polar decomposition of vector fields, preprint, arXiv:1302.2886.
19 H. Heinich, Problème de Monge pour $n$ probabilités, (French) [Monge problem for $n$ probabilities] C. R. Math. Acad. Sci. Paris, 334 (2002), 793-795.       
20 M. Knott and C. Smith, On a generalization of cyclic monotonicity and distances among random vectors, Linear Algebra Appl., 199 (1994), 363-371.       
21 V. Levin, Abstract cyclical monotonicity and Monge solutions for the general Monge-Kantorovich problem, Set-Valued Analysis, 7 (1999), 7-32.       
22 X-N. Ma, N. Trudinger and Wang, X-J., Regularity of potential functions of the optimal transportation problem, Arch. Rational Mech. Anal., 177 (2005), 151-183.       
23 R. McCann, Polar factorization of maps on Riemannian manifolds, Geom. Funct. Anal., 11 (2001), 589-608.       
24 I. Olkin and S. T. Rachev, Maximum submatrix traces for positive definite matrices, SIAM J. Matrix Ana. Appl., 14 (1993), 390-397.       
25 B. Pass, Regularity properties of optimal transportation problems arising in hedonic pricing models, ESAIM Control, Optim. Calc. Var., 19 (2013), 668-678. http://dx.doi.org/10.1051/cocv/2012027.
26 B. Pass, Remarks on the semi-classical Hohenberg-Kohn functional, Nonlinearity, 26 (2013), 2731-2744. http://stacks.iop.org/0951-7715/26/i=9/a=2731.
27 B. Pass, Uniqueness and Monge Solutions in the Multimarginal Optimal Transportation Problem, SIAM Journal on Mathematical Analysis, 43 (2011), 2758-2775.       
28 B. Pass, On the local structure of optimal measures in the multi-marginal optimal transportation problem, Calculus of Variations and Partial Differential Equations, 43 (2012), 529-536.       
29 B. Pass, Optimal transportation with infinitely many marginals, Journal of Functional Analysis, 264 (2013), 947-963.       
30 L. Rüschendorf and L. Uckelmann, On optimal multivariate couplings, Distributions with given marginals and moment problems (Prague, 1996), 261-273, Kluwer Acad. Publ., Dordrecht, 1997.       
31 L. Rüschendorf and L. Uckelmann, On the $n$-coupling problem, J. Multivariate Anal., 81 (2002), 242-258.       
32 C. Villani, "Optimal Transport: Old and New," Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 338. Springer-Verlag, Berlin, 2009. xxii+973 pp.       

Go to top