Abstract Convexity and the Monge-Kantorovich Duality View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2006

AUTHORS

Vladimir L. Levin

ABSTRACT

In the present survey, we reveal links between abstract convex analysis and two variants of the Monge-Kantorovich problem (MKP), with given marginals and with a given marginal difference. It includes: (1) the equivalence of the validity of duality theorems for MKP and appropriate abstract convexity of the corresponding cost functions; (2) a characterization of a (maximal) abstract cyclic monotone map F: X → L ⊂ IRX in terms connected with the constraint set More... »

PAGES

33-72

References to SciGraph publications

  • 1999-03. Abstract Cyclical Monotonicity and Monge Solutions for the General Monge–Kantorovich Problem in SET-VALUED ANALYSIS
  • 2003-08. Abstract Convexity in Measure Theory and in Convex Analysis in JOURNAL OF MATHEMATICAL SCIENCES
  • 2005. The bearing of duality on microeconomics in ADVANCES IN MATHEMATICAL ECONOMICS
  • 1996-03. A superlinear multifunction arising in connection with mass transfer problems in SET-VALUED ANALYSIS
  • 2001-08. On the Monge mass transfer problem in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 2005. A method in demand analysis connected with the Monge—Kantorovich problem in ADVANCES IN MATHEMATICAL ECONOMICS
  • 1996-09. The geometry of optimal transportation in ACTA MATHEMATICA
  • 1998-07. Existence and uniqueness of a measure-preserving optimal mapping in a general Monge-Kantorovich problem in FUNCTIONAL ANALYSIS AND ITS APPLICATIONS
  • 2003. Lecture Notes on Optimal Transport Problems in MATHEMATICAL ASPECTS OF EVOLVING INTERFACES
  • 1997. Foundations of Mathematical Optimization, Convex Analysis without Linearity in NONE
  • Book

    TITLE

    Generalized Convexity and Related Topics

    ISBN

    978-3-540-37006-2

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-540-37007-9_2

    DOI

    http://dx.doi.org/10.1007/978-3-540-37007-9_2

    DIMENSIONS

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