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

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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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     author = {Evans, L. C. and Gomes, D.},
     title = {Linear programming interpretations of {Mather's} variational principle},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {693--702},
     publisher = {EDP-Sciences},
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     year = {2002},
     doi = {10.1051/cocv:2002030},
     zbl = {1090.90143},
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Evans, L. C.; Gomes, D. Linear programming interpretations of Mather's variational principle. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 693-702. doi: 10.1051/cocv:2002030

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