caa a22 4500 475793188 CHVBK 20180406123716.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1007/s001840000052 doi (NATIONALLICENCE)springer-10.1007/s001840000052 Numerical and analytical results for the transportation problem of Monge-Kantorovich [Elektronische Daten] [Ludger Rüschendorf, Ludger Uckelmann] Abstract.: The Monge-Kantorovich transportation problem has a long and interesting history and has found a great variety of applications (see Rachev and Rüschendorf (1998a,b)). Some interesting characterizations of optimal solutions to the transportation problem (resp. coupling problems) have been found recently. For the squared distance and discrete distributions they relate optimal solutions to generalized Voronoi diagrams. Numerically we investigate the dependence of optimal couplings on variations of the coupling function. Numerical results confirm also a conjecture on optimal couplings in the one-dimensional case for nonconvex coupling functions. A proof of this conjecture is given under some technical conditions. Springer-Verlag Berlin Heidelberg, 2000 Key words: optimal couplings nationallicence transportation problem c-convexity nationallicence Rüschendorf Ludger Institut für Mathematische Stochastik, University of Freiburg, Eckerstr. 1, 79104 Freiburg, Germany (e-mail: ruschen@stochastik.uni-freiburg.de), DE aut Uckelmann Ludger Institut für Mathematische Stochastik, University of Freiburg, Eckerstr. 1, 79104 Freiburg, Germany (e-mail: ruschen@stochastik.uni-freiburg.de), DE aut https://doi.org/10.1007/s001840000052 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s001840000052 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Rüschendorf Ludger Institut für Mathematische Stochastik, University of Freiburg, Eckerstr. 1, 79104 Freiburg, Germany (e-mail: ruschen@stochastik.uni-freiburg.de), DE aut NATIONALLICENCE 700 1- Uckelmann Ludger Institut für Mathematische Stochastik, University of Freiburg, Eckerstr. 1, 79104 Freiburg, Germany (e-mail: ruschen@stochastik.uni-freiburg.de), DE aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer