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Rick Chartrand, Kevin R. Vixie, Brendt Wohlberg and Erik M. Bollt, "A gradient descent solution to the Monge-Kantorovich
problem", *Appl. Math. Sci.*, vol. 3, no. 22, pp. 1071--1080, 2009

We present a new, simple, and elegant algorithm for computing the optimal mapping for the Monge-Kantorovich problem with quadratic cost. The method arises from a reformulation of the dual problem into an unconstrained minimization of a convex, continuous functional, for which the derivative can be explicitly found. The Monge-Kantorovich problem has applications in many fields; examples from image warping and medical imaging are shown.

@article{chartrand-2009-gradient,

author = {Rick Chartrand and Kevin R. Vixie and Brendt Wohlberg and Erik M. Bollt},

title = {A gradient descent solution to the {M}onge-{K}antorovich
problem},

year = {2009},

urlpdf = {http://brendt.wohlberg.net/publications/pdf/chartrand-2009-gradient.pdf},

journal = {Appl. Math. Sci.},

volume = {3},

number = {22},

pages = {1071--1080}

}