Linear programming interpretations of Mather's variational principle

Evans, L. C.; Gomes, D.

doi:10.1051/cocv:2002030

Evans, L. C. ; Gomes, D.

ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002) , pp. 693-702.

Résumé

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].

EuDML 244650 | Zbl 1090.90143 | 1 citation dans Numdam

DOI : https://doi.org/10.1051/cocv:2002030
Classification : 90C05, 35F20
Mots clés : linear programming, duality, weak KAM theory

@article{COCV_2002__8__693_0,
     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},
     volume = {8},
     year = {2002},
     doi = {10.1051/cocv:2002030},
     zbl = {1090.90143},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2002__8__693_0/}
}

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. http://www.numdam.org/item/COCV_2002__8__693_0/

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