Linear programming interpretations of Mather's variational principle
ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002), pp. 693-702.

We discuss some implications of linear programming for Mather theory [13, 14, 15] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an n-dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [6, 7, 8, 5].

DOI: 10.1051/cocv:2002030
Classification: 90C05, 35F20
Keywords: linear programming, duality, weak KAM theory
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Evans, L. C.; Gomes, D. Linear programming interpretations of Mather's variational principle. ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002), pp. 693-702. doi : 10.1051/cocv:2002030. http://archive.numdam.org/articles/10.1051/cocv:2002030/

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