Analytic solutions for the approximated 1-D Kantorovich mass transfer problems

Abstract

This paper mainly investigates the approximation of a global maximizer of the 1-D Monge-Kantorovich mass transfer problem through the approach of nonlinear differential equations with Dirichlet boundary. Using an approximation mechanism, the primal maximization problem can be transformed into a sequence of minimization problems. By applying the canonical duality theory, one is able to derive a sequence of analytic solutions for the minimization problems. In the final analysis, the convergence of the sequence to a global maximizer of the primal Monge-Kantorovich problem will be demonstrated.

10 pages, 0 figure. arXiv admin note: text overlap with arXiv:1607.06554, arXiv:1607.06557