This note deals with the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction presented in [7]. We emphasize the measurability assumption on the hidden structure of linear preorder. Résumé. Dans la présente note nous décrivons brièvement la construction introduite dans [7] à propo...

This paper considers linear functions constructed on two different weighted branching processes and provides explicit bounds for their Kantorovich-Rubinstein distance in terms of couplings of their corresponding generic branching vectors. Motivated by applications to the analysis of random graphs, we also consider a variation of the weighted branching process where the generic branching vector ...

We propose the use of the Kantorovich-Rubinstein norm from optimal transport in imaging problems. In particular, we discuss a variational regularisation model endowed with a Kantorovich-Rubinstein discrepancy term and total variation regularization in the context of image denoising and cartoon-texture decomposition. We point out connections of this approach to several other recently proposed me...

The Monge-Kantorovich mass transfer problem is equivalently formulated as an optimal control prblem for the mass transport equation. The equivalency of the two problems is establish using the Lax-Hopf formula and the optimal control theory arguments. Also, it is shown that the optimal solution to the equivalent control problem is given in a gradient form in terms of the potential solution to th...

This paper proposes a parallel solver for the nonlinear systems in Bernstein form based on subdivision and the Newton-Raphson method, where the Kantorovich theorem is employed to identify the existence of a unique root and guarantee convergence of the Newton-Raphson iterations. Since the Kantorovich theorem accommodates a singular Jacobian at the root, the proposed algorithm performs well in a ...

In the present paper, we deal with approximation properties of semi-exponential Sz?sz-Mirakyan-Kantorovich operators. Here, establish relation between Sz?sz-Mirakyan operators and its Kantorovich variant. Further, propose modification variant so as to preserve test functions eAx e2Ax derive Voronovskaya-type result.

We prove several multiplicative inequalities relating the Kantorovich norm with the Sobolev norm for functions on a Riemannian manifold satisfying certain curvature conditions.