Linear programming interpretations of mather's variational principle

L. C. Evans; D. Gomes

doi:10.1051/cocv:2002030

Linear programming interpretations of mather's variational principle

L. C. Evans^*, D. Gomes

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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].

Original language	English (US)
Pages (from-to)	693-702
Number of pages	10
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	8
DOIs	https://doi.org/10.1051/cocv:2002030
State	Published - Jun 2002
Externally published	Yes

Keywords

Duality
Linear programming
Weak KAM theory

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization
Computational Mathematics

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10.1051/cocv:2002030

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title = "Linear programming interpretations of mather's variational principle",

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].",

keywords = "Duality, Linear programming, Weak KAM theory",

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

year = "2002",

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doi = "10.1051/cocv:2002030",

language = "English (US)",

volume = "8",

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AU - Evans, L. C.

AU - Gomes, D.

PY - 2002/6

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N2 - 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].

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].

KW - Duality

KW - Linear programming

KW - Weak KAM theory

UR - http://www.scopus.com/inward/record.url?scp=2442648253&partnerID=8YFLogxK

U2 - 10.1051/cocv:2002030

DO - 10.1051/cocv:2002030

M3 - Article

AN - SCOPUS:2442648253

SN - 1292-8119

VL - 8

SP - 693

EP - 702

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

ER -

Linear programming interpretations of mather's variational principle

Abstract

Keywords

ASJC Scopus subject areas

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