Computing the effective hamiltonian using a variational approach

Diogo A. Gomes; Adam M. Oberman

doi:10.1109/CDC.2005.1582243

Computing the effective hamiltonian using a variational approach

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

A numerical method for homogenization of Hamilton-Jacobi equations is presented and implemented as an L^∞ calculus of variations problem. Solutions are found by solving a nonlinear convex optimization problem. The numerical method is shown to be convergent and error estimates are provided. Several examples are worked in detail, including the cases of non-strictly convex Hamiltonians and Hamiltonians for which the cell problem has no solution.

Original language	English (US)
Title of host publication	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages	729-733
Number of pages	5
DOIs	https://doi.org/10.1109/CDC.2005.1582243
State	Published - 2005
Externally published	Yes
Event	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain Duration: Dec 12 2005 → Dec 15 2005

Publication series

Name	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume	2005

Other

Other	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Country/Territory	Spain
City	Seville
Period	12/12/05 → 12/15/05

ASJC Scopus subject areas

General Engineering

Access to Document

10.1109/CDC.2005.1582243

Cite this

Gomes, D. A., & Oberman, A. M. (2005). Computing the effective hamiltonian using a variational approach. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 729-733). Article 1582243 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005). https://doi.org/10.1109/CDC.2005.1582243

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title = "Computing the effective hamiltonian using a variational approach",

abstract = "A numerical method for homogenization of Hamilton-Jacobi equations is presented and implemented as an L∞ calculus of variations problem. Solutions are found by solving a nonlinear convex optimization problem. The numerical method is shown to be convergent and error estimates are provided. Several examples are worked in detail, including the cases of non-strictly convex Hamiltonians and Hamiltonians for which the cell problem has no solution.",

author = "Gomes, {Diogo A.} and Oberman, {Adam M.}",

year = "2005",

doi = "10.1109/CDC.2005.1582243",

language = "English (US)",

isbn = "0780395689",

series = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

pages = "729--733",

booktitle = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

note = "44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 ; Conference date: 12-12-2005 Through 15-12-2005",

}

Gomes, DA & Oberman, AM 2005, Computing the effective hamiltonian using a variational approach. in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05., 1582243, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, vol. 2005, pp. 729-733, 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, Seville, Spain, 12/12/05. https://doi.org/10.1109/CDC.2005.1582243

Computing the effective hamiltonian using a variational approach. / Gomes, Diogo A.; Oberman, Adam M.
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 729-733 1582243 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - A numerical method for homogenization of Hamilton-Jacobi equations is presented and implemented as an L∞ calculus of variations problem. Solutions are found by solving a nonlinear convex optimization problem. The numerical method is shown to be convergent and error estimates are provided. Several examples are worked in detail, including the cases of non-strictly convex Hamiltonians and Hamiltonians for which the cell problem has no solution.

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M3 - Conference contribution

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T3 - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

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BT - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

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Gomes DA, Oberman AM. Computing the effective hamiltonian using a variational approach. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 729-733. 1582243. (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05). doi: 10.1109/CDC.2005.1582243

Computing the effective hamiltonian using a variational approach

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