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Fundamentals in Discrete Convex Analysis

Author Kazuo Murota



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Kazuo Murota

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Kazuo Murota. Fundamentals in Discrete Convex Analysis. In Computing and Markets. Dagstuhl Seminar Proceedings, Volume 5011, pp. 1-2, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2005)
https://doi.org/10.4230/DagSemProc.05011.10

Abstract

This talk describes fundamental properties of M-convex and L-convex functions that play the central roles in discrete convex analysis. These concepts were originally introduced in combinatorial optimization, but turned out to be relevant in economics. Emphasis is put on discrete duality and conjugacy respect to the Legendre-Fenchel transformation. Monograph information: http://www.misojiro.t.u-tokyo.ac.jp/~murota/mybooks.html#DCAsiam2003
Keywords
  • gross substitute
  • discrete convex functions
  • M-convex function
  • Fenchel-Legendre transformation

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