Characterization of the Optimal Plans for the Monge-kantorovich Transport Problem

نویسنده

  • CHRISTIAN LÉONARD
چکیده

We present a general method, based on conjugate duality, for solving a convex minimization problem without assuming unnecessary topological restrictions on the constraint set. It leads to dual equalities and characterizations of the minimizers without constraint qualification. As an example of application, the Monge-Kantorovich optimal transport problem is solved in great detail. In particular, the optimal transport plans are characterized without restriction. This characterization improves the already existing literature on the subject.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Characterization of Optimal Transport Plans for the Monge-kantorovich-problem

We prove that c-cyclically monotone transport plans π optimize the Monge-Kantorovich transportation problem under an additional measurability condition. This measurability condition is always satisfied for finitely valued, lower semi-continuous cost functions. In particular, this yields a positive answer to Problem 2.25 in C. Villani’s book. We emphasize that we do not need any regularity condi...

متن کامل

A saddle-point approach to the Monge-Kantorovich optimal transport problem

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...

متن کامل

AN EXISTENCE RESULT FOR THE MONGE PROBLEM IN n WITH NORM COST FUNCTIONS

We establish existence of solutions to the Monge problem in n with a norm cost function, assuming absolute continuity of the initial measure. The loss in strict convexity of the unit ball implies that transport is possible along several directions. As in [4], we single out particular solutions to the Kantorovich relaxation with a secondary variational problem, which involves a strictly convex n...

متن کامل

On Fluid mechanics formulation of Monge-Kantorovich Mass Transfer Problem

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...

متن کامل

Mathematical Analysis ON OPTIMALITY OF c-CYCLICALLY MONOTONE TRANSFERENCE PLANS SUR L’OPTIMALITÉ DES PLANS DE TRANSPORT c-CYCLIQUES MONOTONES

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...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006