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

Handle URI:
http://hdl.handle.net/10754/597541
Title:
An optimal L1-minimization algorithm for stationary Hamilton-Jacobi equations
Authors:
Guermond, Jean-Luc; Popov, Bojan
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.
Publisher:
International Press of Boston
Journal:
Communications in Mathematical Sciences
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
2009
DOI:
10.4310/cms.2009.v7.n1.a11
Type:
Article
ISSN:
1539-6746; 1945-0796
Sponsors:
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).
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorGuermond, Jean-Lucen
dc.contributor.authorPopov, Bojanen
dc.date.accessioned2016-02-25T12:41:43Zen
dc.date.available2016-02-25T12:41:43Zen
dc.date.issued2009en
dc.identifier.issn1539-6746en
dc.identifier.issn1945-0796en
dc.identifier.doi10.4310/cms.2009.v7.n1.a11en
dc.identifier.urihttp://hdl.handle.net/10754/597541en
dc.description.abstractWe 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.en
dc.description.sponsorshipThis 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).en
dc.publisherInternational Press of Bostonen
dc.titleAn optimal L1-minimization algorithm for stationary Hamilton-Jacobi equationsen
dc.typeArticleen
dc.identifier.journalCommunications in Mathematical Sciencesen
dc.contributor.institutionDepartment of Mathematics, Texas A&M University 3368 TAMU, College Station, TX 77843, USA. On leave from LIMSI, UPRR 3251 CNRS, BP 133, 91403 Orsay cedex, Franceen
dc.contributor.institutionDepartment of Mathematics, Texas A&M University 3368 TAMU, College Station, TX 77843, USAen
kaust.grant.numberKUS-C1-016-04en
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