# Linear programming interpretations of Mather’s variational principle

ESAIM: Control, Optimisation and Calculus of Variations (2002)

- Volume: 8, page 693-702
- ISSN: 1292-8119

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topEvans, L. C., and Gomes, D.. "Linear programming interpretations of Mather’s variational principle." ESAIM: Control, Optimisation and Calculus of Variations 8 (2002): 693-702. <http://eudml.org/doc/244650>.

@article{Evans2002,

abstract = {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].},

author = {Evans, L. C., Gomes, D.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {linear programming; duality; weak KAM theory},

language = {eng},

pages = {693-702},

publisher = {EDP-Sciences},

title = {Linear programming interpretations of Mather’s variational principle},

url = {http://eudml.org/doc/244650},

volume = {8},

year = {2002},

}

TY - JOUR

AU - Evans, L. C.

AU - Gomes, D.

TI - Linear programming interpretations of Mather’s variational principle

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2002

PB - EDP-Sciences

VL - 8

SP - 693

EP - 702

AB - 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].

LA - eng

KW - linear programming; duality; weak KAM theory

UR - http://eudml.org/doc/244650

ER -

## References

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- [6] A. Fathi, Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens. C. R. Acad. Sci. Paris Sér. I Math. 324 (1997) 1043-1046. Zbl0885.58022MR1451248
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- [10] D. Gomes, Numerical methods and Hamilton–Jacobi equations (to appear).
- [11] P. Lax, Linear Algebra. John Wiley (1997). Zbl0904.15001MR1423602
- [12] P.-L. Lions, G. Papanicolaou and S.R.S. Varadhan, Homogenization of Hamilton–Jacobi equations. CIRCA (1988) (unpublished).
- [13] J. Mather, Minimal measures. Comment. Math Helvetici 64 (1989) 375-394. Zbl0689.58025MR998855
- [14] J. Mather, Action minimizing invariant measures for positive definite Lagrangian systems. Math. Z. 207 (1991) 169-207. Zbl0696.58027MR1109661
- [15] J. Mather and G. Forni, Action minimizing orbits in Hamiltonian systems. Transition to Chaos in Classical and Quantum Mechanics, edited by S. Graffi. Sringer, Lecture Notes in Math. 1589 (1994). Zbl0822.70011MR1323222

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