An optimal L1-minimization algorithm for stationary Hamilton-Jacobi equations

Jean-Luc Guermond; Bojan Popov

doi:10.4310/cms.2009.v7.n1.a11

An optimal L1-minimization algorithm for stationary Hamilton-Jacobi equations

Jean-Luc Guermond, Bojan Popov

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

3 Scopus citations

Abstract

We describe an algorithm for solving steady one-dimensional convex-like Hamilton-Jacobi equations using a L1-minimization technique on piecewise linear approximations. For a large class of convex Hamiltonians, the algorithm is proven to be convergent and of optimal complexity whenever the viscosity solution is q-semiconcave. Numerical results are presented to illustrate the performance of the method.

Original language	English (US)
Pages (from-to)	211-238
Number of pages	28
Journal	Communications in Mathematical Sciences
Volume	7
Issue number	1
DOIs	https://doi.org/10.4310/cms.2009.v7.n1.a11
State	Published - 2009
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This material is based upon work supported by the National Science Foundation grant DMS-0510650.This publication is based on work supported by Award No. KUS-C1-016-04, made by King AbdullahUniversity of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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abstract = "We describe an algorithm for solving steady one-dimensional convex-like Hamilton-Jacobi equations using a L1-minimization technique on piecewise linear approximations. For a large class of convex Hamiltonians, the algorithm is proven to be convergent and of optimal complexity whenever the viscosity solution is q-semiconcave. Numerical results are presented to illustrate the performance of the method.",

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doi = "10.4310/cms.2009.v7.n1.a11",

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AU - Popov, Bojan

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N2 - We describe an algorithm for solving steady one-dimensional convex-like Hamilton-Jacobi equations using a L1-minimization technique on piecewise linear approximations. For a large class of convex Hamiltonians, the algorithm is proven to be convergent and of optimal complexity whenever the viscosity solution is q-semiconcave. Numerical results are presented to illustrate the performance of the method.

AB - We describe an algorithm for solving steady one-dimensional convex-like Hamilton-Jacobi equations using a L1-minimization technique on piecewise linear approximations. For a large class of convex Hamiltonians, the algorithm is proven to be convergent and of optimal complexity whenever the viscosity solution is q-semiconcave. Numerical results are presented to illustrate the performance of the method.

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JO - Communications in Mathematical Sciences

JF - Communications in Mathematical Sciences

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An optimal L1-minimization algorithm for stationary Hamilton-Jacobi equations

Abstract

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