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On the Existence of Optima in Complete Chains and Lattices

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  • Nikolai S. Kukushkin

    () (Russian Academy of Sciences)

Abstract

A necessary and sufficient condition for a preference ordering defined on a chain-complete poset to attain its maximum in every subcomplete chain is obtained. A meet-superextremal, or join-superextremal, function on a complete lattice attains its maximum in every subcomplete sublattice if and only if it attains a maximum in every subcomplete chain.

Suggested Citation

  • Nikolai S. Kukushkin, 2012. "On the Existence of Optima in Complete Chains and Lattices," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 759-767, September.
  • Handle: RePEc:spr:joptap:v:154:y:2012:i:3:d:10.1007_s10957-012-0031-8
    DOI: 10.1007/s10957-012-0031-8
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    References listed on IDEAS

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    1. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    2. Kukushkin, Nikolai S., 2008. "Maximizing an interval order on compact subsets of its domain," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 195-206, September.
    3. Nikolai Kukushkin, 2013. "Monotone comparative statics: changes in preferences versus changes in the feasible set," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 1039-1060, April.
    4. Smith, Tony E, 1974. "On the Existence of Most-Preferred Alternatives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 184-194, February.
    5. Nikolai S Kukushkin, 2005. "On the existence of maximal elements: An impossibility theorem," Game Theory and Information 0509004, University Library of Munich, Germany.
    6. Marco LiCalzi & Arthur F. Veinott, 2005. "Subextremal functions and lattice programming," GE, Growth, Math methods 0509001, University Library of Munich, Germany.
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    Cited by:

    1. Nikolai S. Kukushkin, 2019. "On the existence of undominated alternatives in convex sets," Economics Bulletin, AccessEcon, vol. 39(3), pages 2129-2136.

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