RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Funktsional. Anal. i Prilozhen., 2002, Volume 36, Issue 2, Pages 38–44 (Mi faa189)  

This article is cited in 1 scientific paper (total in 1 paper)

Optimality Conditions for Smooth Monge Solutions of the Monge–Kantorovich problem

V. L. Levin

Central Economics and Mathematics Institute, RAS

Abstract: The Monge–Kantorovich problem (MKP) with given marginals defined on closed domains $X\subset\mathbb{R}^n$, $Y\subset\mathbb{R}^m$ and a smooth cost function $c\colon X\times Y\to\mathbb{R}$ is considered. Conditions are obtained (both necessary ones and sufficient ones) for the optimality of a Monge solution generated by a smooth measure-preserving map $f\colon X\to Y$. The proofs are based on an optimality criterion for a general MKP in terms of nonemptiness of the sets $Q_0(\zeta)=\{u\in\mathbb{R}^X:u(x)-u(z)\le\zeta(x,z)$ for all $x,z\in X\}$ for special functions $\zeta$ on $X\times X$ generated by $c$ and $f$. Also, earlier results by the author are used when considering the above-mentioned nonemptiness conditions for the case of smooth $\zeta$.

Keywords: Monge–Kantorovich problem, marginal, Monge solution

DOI: https://doi.org/10.4213/faa189

Full text: PDF file (129 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2002, 36:2, 114–119

Bibliographic databases:

UDC: 517.9
Received: 25.10.2001

Citation: V. L. Levin, “Optimality Conditions for Smooth Monge Solutions of the Monge–Kantorovich problem”, Funktsional. Anal. i Prilozhen., 36:2 (2002), 38–44; Funct. Anal. Appl., 36:2 (2002), 114–119

Citation in format AMSBIB
\Bibitem{Lev02}
\by V.~L.~Levin
\paper Optimality Conditions for Smooth Monge Solutions of the Monge--Kantorovich problem
\jour Funktsional. Anal. i Prilozhen.
\yr 2002
\vol 36
\issue 2
\pages 38--44
\mathnet{http://mi.mathnet.ru/faa189}
\crossref{https://doi.org/10.4213/faa189}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1922017}
\zmath{https://zbmath.org/?q=an:1021.49029}
\elib{http://elibrary.ru/item.asp?id=14146864}
\transl
\jour Funct. Anal. Appl.
\yr 2002
\vol 36
\issue 2
\pages 114--119
\crossref{https://doi.org/10.1023/A:1015666422861}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000176341200004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0036273401}


Linking options:
  • http://mi.mathnet.ru/eng/faa189
  • https://doi.org/10.4213/faa189
  • http://mi.mathnet.ru/eng/faa/v36/i2/p38

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. L. Levin, “Optimality conditions and exact solutions to the two-dimensional Monge–Kantorovich problem”, J. Math. Sci. (N. Y.), 133:4 (2006), 1456–1463  mathnet  crossref  mathscinet  zmath  elib  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
    Number of views:
    This page:394
    Full text:138
    References:51

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020