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Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 6, Pages 999–1000 (Mi zvmmf9616)  

This article is cited in 2 scientific papers (total in 2 papers)

Supermodular programming on finite lattices

V. R. Khachaturov, Roman V. Khachaturov, Ruben V. Khachaturov

Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow

Abstract: There is a discription of the problems of minimization of supermodular functions on the different types of lattices: Boolean lattices, lattices with relative supplements (division lattices, lattices of vector subspaces of finite-dimensional vector space, geometrical lattices), lattices equal to Cartesian product of chains. The previously obtained theoretical results, on the basis of which the problems of minimization of supermodular functions on these lattices have been solved, are shown. A new type of lattices, lattice of Cubes, is defined and described. The problems of minimization and maximization of supermodular functions are considered on it. Particular examples of such functions are given. Optimization algorithms and the possibilities of setting and solving a new class of problems on the lattices of Cubes are discussed.

Key words: descrete optimization, finite lattices, Boolean, Hyper-Cube, supermodular programming

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:6, 855–878

Bibliographic databases:

UDC: 519.854
Received: 19.08.2011

Citation: V. R. Khachaturov, Roman V. Khachaturov, Ruben V. Khachaturov, “Supermodular programming on finite lattices”, Zh. Vychisl. Mat. Mat. Fiz., 52:6 (2012), 999–1000; Comput. Math. Math. Phys., 52:6 (2012), 855–878

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. M. Montlevich, “O submodulyarnosti funktsii pribyli v odnoi iz zadach planirovaniya perevozok”, Vestn. SamGU. Estestvennonauchn. ser., 2014, no. 10(121), 48–54  mathnet
    2. A. G. Perevozchikov, V. Yu. Reshetov, A. I. Lesik, “Neodnorodnaya igra «napadenie-oborona» na osnove obobschennogo printsipa uravnivaniya”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2018, no. 1, 89–106  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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