The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to c-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes infinite values. It leads us to new explicit sufficient and necessary optimality conditions. As by-products, we obtain a new proof of the well-known Kantorovich du...

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...

Starting with a positive linear operator we apply the Kantorovich modification and related modification. The resulting operators are investigated. We interested in eigenstructure, Voronovskaya formula, induced generalized convexity, invariant measures iterates. Some known results from literature extended.

This article presents the derivation of elastic buckling equations and boundary conditions shear-deformable plates in frame extended Kantorovich method (EKM). Surveying literature shows that those stability are often obtained using a wrong by confusing them with linear equilibrium condition. work aims at providing correct is built on Buckling derived for three different plate theories, namely, ...

An analytical approach is proposed in the reduction of free edge peeling stresses of laminated composites using active piezoelectric layers. The approach is the extended Kantorovich method which is an iterative method. Multiterms of trial function are employed and governing equations are derived by taking the principle of complementary virtual work. The solutions are obtained by solving a gener...

The extended principle of minimal action is described in the presence of prescribed source and sink points. Under the assumption of zero net flux, it leads to an optimal Monge-Kantorovich transport problem of metric type. We concentrate on action corresponding to a mecahnical Lagrangian. The optimal solution turns out to be a measure supprted on a graph composed of geodesic arcs connecting pair...

Boundary value problems posed over thin solids are often amenable to a dimensional reduction in that one or more spatial dimensions may be eliminated from the governing equation. One of the popular methods of achieving dimensional reduction is the Kantorovich method, where based on certain a priori assumptions, a lower-dimensional problem over a ‘mid-element’ is obtained. Unfortunately, the mid...

Boundary value problems posed over thin solids are often amenable to a dimensional reduction in that one or more spatial dimensions may be eliminated from the governing equation. One of the popular methods of achieving dimensional reduction is the Kantorovich method, where based on certain a priori assumptions, a lower-dimensional problem over a ‘mid-element’ is obtained. Unfortunately, the mid...