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Subextremal functions and lattice programming

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Author Info

  • Marco LiCalzi

    (University of Venice, Italy)

  • Arthur F. Veinott

    (Stanford University)

Abstract

Let M and N be the set of minimizers of a function f over respective subsets K and L of a lattice, with K being lower than L. This paper characterizes the class of functions f for which M is lower (resp., weakly lower, meet lower, join lower, chain lower) than N for all K lower than L. The resulting five classes of functions, called subextremal variants, have alternate characterizations by variants of the downcrossing-differences property, i.e., their first differences change sign at most once from plus to minus along complementary chains.

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Bibliographic Info

Paper provided by EconWPA in its series GE, Growth, Math methods with number 0509001.

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Length: 21 pages
Date of creation: 04 Sep 2005
Date of revision:
Handle: RePEc:wpa:wuwpge:0509001

Note: Type of Document - pdf; pages: 21. 21 pages, scanned from original on paper to a PDF
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Web page: http://128.118.178.162

Related research

Keywords: Comparative statics; supermodular functions;

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Cited by:
  1. Manjira Datta & Leonard J. Mirman & Olivier F. Morand & Kevin L. Reffett, 2002. "Monotone Methods for Markovian Equilibrium in Dynamic Economies," Tinbergen Institute Discussion Papers 02-086/2, Tinbergen Institute.
  2. Manjira Datta & Leonard Mirman & Kevin Reffett, . "Nonclassical Brock-Mirman Economies," Working Papers 2179544, Department of Economics, W. P. Carey School of Business, Arizona State University.
  3. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
  4. Elena Antoniadou, 2007. "Comparative Statics for the Consumer Problem," Economic Theory, Springer, vol. 31(1), pages 189-203, April.
  5. Koji Shirai, 2008. "A generalization of monotone comparative statics," Economics Bulletin, AccessEcon, vol. 3(39), pages 1-9.
  6. Manjira Datta & Kevin L. Reffett, 2005. "Isotone Recursive Methods: the Case of Homogeneous Agents," Tinbergen Institute Discussion Papers 05-012/2, Tinbergen Institute.

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