Multiresolution Analysis Applied to the Monge-Kantorovich Problem

Multivariate Monge-Kantorovich Transportation Problem

Received: January 6, 2011 Accepted: January 24, 2011 doi:10.5539/jmr.v3n2p66 The research is supported by Zhejiang Provincial Education Department research projects (Y201016421) Abstract Monge-Kantorovich transportation problem in a bounded region of Euclidean space is transferred into a partial differential equations group. And then the explicit formula of the optimal coupling is achieved. The...

On Monge - Kantorovich Problem in the Plane

We transfer the celebrating Monge-Kontorovich problem in a bounded domain of Euclidean plane into a Dirichlet boundary problem associated to a quasi-linear elliptic equation with 0−order term missing in its diffusion coefficients: A(x, F ′ x )F ′′ xx +B(y, F ′ y )F ′′ yy = C(x, y, F ′ x , F ′ y ) where A(., .) > 0, B(., .) > 0 and C are functions based on the initial distributions, F is an unkn...

Minimizing Flows for the Monge-Kantorovich Problem

A Gradient Descent Solution to the Monge-Kantorovich Problem

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 ima...

Monge–Kantorovich transportation problem and optimal couplings

• Mathematics Subject Classification: 60E15, 90C40, 49N15 •