# Linear programming interpretations of Mather's variational principle

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- 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 (2010): 693-702. <http://eudml.org/doc/90665>.

@article{Evans2010,

abstract = {
We discuss some implications of linear programming for Mather theory
[13-15] 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 [5-8].
},

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

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

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

language = {eng},

month = {3},

pages = {693-702},

publisher = {EDP Sciences},

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

url = {http://eudml.org/doc/90665},

volume = {8},

year = {2010},

}

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

DA - 2010/3//

PB - EDP Sciences

VL - 8

SP - 693

EP - 702

AB -
We discuss some implications of linear programming for Mather theory
[13-15] 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 [5-8].

LA - eng

KW - Linear programming; duality; weak KAM theory.; linear programming; weak KAM theory

UR - http://eudml.org/doc/90665

ER -

## References

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- 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.
- A. Fathi, Solutions KAM faibles conjuguées et barrières de Peierls. C. R. Acad. Sci. Paris Sér. I Math.325 (1997) 649-652.
- A. Fathi, Weak KAM theory in Lagrangian Dynamics, Preliminary Version. Lecture Notes (2001).
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- D. Gomes, Numerical methods and Hamilton-Jacobi equations (to appear).
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- J. Mather, Minimal measures. Comment. Math Helvetici64 (1989) 375-394.
- J. Mather, Action minimizing invariant measures for positive definite Lagrangian systems. Math. Z.207 (1991) 169-207.
- 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).

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