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 Mat. Sb., 2006, Volume 197, Number 9, Pages 103–114 (Mi msb1492)

Best approximation problems relating to Monge–Kantorovich duality

V. L. Levin

Central Economics and Mathematics Institute, RAS

Abstract: Problems of the best approximation of bounded continuous functions on a topological space $X\times X$ by functions of the form $u(x)-u(y)$ are considered. Formulae for the values of the best approximations are obtained and the equivalence between the existence of precise solutions and the non-emptiness of the constraint set of the auxiliary dual Monge–Kantorovich problem with a special cost function is established. The form of precise solutions is described in terms relating to the Monge–Kantorovich duality, and for several classes of approximated functions the existence of precise solutions with additional properties, such as smoothness and periodicity, is proved.
Bibliography: 20 titles.

DOI: https://doi.org/10.4213/sm1492

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English version:
Sbornik: Mathematics, 2006, 197:9, 1353–1364

Bibliographic databases:

UDC: 517.972.8
MSC: 41A50, 49N15

Citation: V. L. Levin, “Best approximation problems relating to Monge–Kantorovich duality”, Mat. Sb., 197:9 (2006), 103–114; Sb. Math., 197:9 (2006), 1353–1364

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb1492
• https://doi.org/10.4213/sm1492
• http://mi.mathnet.ru/eng/msb/v197/i9/p103

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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. Levin V.L., “Smooth feasible solutions to a dual Monge-Kantorovich problem and their application to the best approximation and mathematical economics problems”, Dokl. Math., 77:2 (2008), 281–283
2. Levin V.L., “Dvoistvennost Monzha–Kantorovicha i ee primenenie v teorii poleznosti”, Ekonomika i matematicheskie metody, 47:4 (2011), 143–165
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