Ordinal optimization: Difference between revisions

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== Mathematical foundations ==

{{See also|Mathematical optimization|Partially ordered set|Lattice (order)|Greedoid|Antimatroid|Combinatorial optimization|Duality (mathematics)#Order-reversing dualities}}

Ordinal optimization is the maximization of function taking values in a [[partially ordered set]] ("poset") — or, [[duality (mathematics)#Order-reversing dualities|dually]], the minimization of functions taking values in a poset.<ref>Dietrich, B. L.; Hoffman, A. J. On greedy algorithms, partially ordered sets, and submodular functions. ''IBM J. Res. Develop.'' 47 (2003), no. 1, 25–30. <!-- MR1957350 (2003k:90102) --></ref><ref>Topkis, Donald M. ''Supermodularity and complementarity''. Frontiers of Economic Research. Princeton University Press, Princeton, NJ, 1998. xii+272 pp. ISBN 0-691-03244-0 <!-- MR1614637 (99i:90024) --></ref><ref>Singer, Ivan ''Abstract convex analysis''. Canadian Mathematical Society Series of Monographs and Advanced Texts. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1997. xxii+491 pp. ISBN 0-471-16015-6 <!-- MR1461544 --></ref><ref>Björner, Anders; Ziegler, Günter M. Introduction to greedoids. ''Matroid applications'', 284–357, Encyclopedia Math. Appl., 40, Cambridge Univ. Press, Cambridge, 1992,<!-- MR1165545 (94a:05038) --></ref>