A semi-Lagrangian scheme for Hamilton-Jacobi-Bellman equations with oblique boundary conditions
We investigate in this work a fully-discrete semi-Lagrangian approximation of second order possibly degenerate Hamilton-Jacobi-Bellman (HJB) equations on a bounded domain with oblique boundary conditions. These equations appear naturally in the study of optimal control of diffusion processes with ob...
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| creator | Calzola, Elisa Carlini, Elisabetta Dupuis, Xavier Silva, Francisco J |
| description | We investigate in this work a fully-discrete semi-Lagrangian approximation of
second order possibly degenerate Hamilton-Jacobi-Bellman (HJB) equations on a
bounded domain with oblique boundary conditions. These equations appear
naturally in the study of optimal control of diffusion processes with oblique
reflection at the boundary of the domain.
The proposed scheme is shown to satisfy a consistency type property, it is
monotone and stable. Our main result is the convergence of the numerical
solution towards the unique viscosity solution of the HJB equation. The
convergence result holds under the same asymptotic relation between the time
and space discretization steps as in the classical setting for semi-Lagrangian
schemes. We present some numerical results that confirm the numerical
convergence of the scheme. |
| doi_str_mv | 10.48550/arxiv.2109.10228 |
| format | Article |
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second order possibly degenerate Hamilton-Jacobi-Bellman (HJB) equations on a
bounded domain with oblique boundary conditions. These equations appear
naturally in the study of optimal control of diffusion processes with oblique
reflection at the boundary of the domain.
The proposed scheme is shown to satisfy a consistency type property, it is
monotone and stable. Our main result is the convergence of the numerical
solution towards the unique viscosity solution of the HJB equation. The
convergence result holds under the same asymptotic relation between the time
and space discretization steps as in the classical setting for semi-Lagrangian
schemes. We present some numerical results that confirm the numerical
convergence of the scheme.</description><identifier>DOI: 10.48550/arxiv.2109.10228</identifier><language>eng</language><subject>Computer Science - Numerical Analysis ; Mathematics - Numerical Analysis</subject><creationdate>2021-09</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2109.10228$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2109.10228$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Calzola, Elisa</creatorcontrib><creatorcontrib>Carlini, Elisabetta</creatorcontrib><creatorcontrib>Dupuis, Xavier</creatorcontrib><creatorcontrib>Silva, Francisco J</creatorcontrib><title>A semi-Lagrangian scheme for Hamilton-Jacobi-Bellman equations with oblique boundary conditions</title><description>We investigate in this work a fully-discrete semi-Lagrangian approximation of
second order possibly degenerate Hamilton-Jacobi-Bellman (HJB) equations on a
bounded domain with oblique boundary conditions. These equations appear
naturally in the study of optimal control of diffusion processes with oblique
reflection at the boundary of the domain.
The proposed scheme is shown to satisfy a consistency type property, it is
monotone and stable. Our main result is the convergence of the numerical
solution towards the unique viscosity solution of the HJB equation. The
convergence result holds under the same asymptotic relation between the time
and space discretization steps as in the classical setting for semi-Lagrangian
schemes. We present some numerical results that confirm the numerical
convergence of the scheme.</description><subject>Computer Science - Numerical Analysis</subject><subject>Mathematics - Numerical Analysis</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj7tOwzAYRr0woMIDMOEXcLDjOLXHUgEFRWLpHv2_L62lxKa5cHl7Suj0LUefziHkTvCi0krxBxi-42dRCm4KwctSX5N2Q0ffR9bAYYB0iJDoaI--9zTkge6gj92UE3sDmzGyR991_RnxpxmmmNNIv-J0pBm7eJo9xTwnB8MPtTm5uAA35CpAN_rby67I_vlpv92x5v3ldbtpGNRrzTRKUeta1q6yxmAIykln0KKW1onSoVIePCqJ2gdeIhi3FgG9MrJSoJRckfv_26Ww_Rhif_Zo_0rbpVT-AvIYUIQ</recordid><startdate>20210921</startdate><enddate>20210921</enddate><creator>Calzola, Elisa</creator><creator>Carlini, Elisabetta</creator><creator>Dupuis, Xavier</creator><creator>Silva, Francisco J</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20210921</creationdate><title>A semi-Lagrangian scheme for Hamilton-Jacobi-Bellman equations with oblique boundary conditions</title><author>Calzola, Elisa ; Carlini, Elisabetta ; Dupuis, Xavier ; Silva, Francisco J</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a678-8b3168636d4c99bff5d3d9bcb83cd12db55eaeb53b8ef02ba9d71fbe59345a553</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Computer Science - Numerical Analysis</topic><topic>Mathematics - Numerical Analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Calzola, Elisa</creatorcontrib><creatorcontrib>Carlini, Elisabetta</creatorcontrib><creatorcontrib>Dupuis, Xavier</creatorcontrib><creatorcontrib>Silva, Francisco J</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Calzola, Elisa</au><au>Carlini, Elisabetta</au><au>Dupuis, Xavier</au><au>Silva, Francisco J</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A semi-Lagrangian scheme for Hamilton-Jacobi-Bellman equations with oblique boundary conditions</atitle><date>2021-09-21</date><risdate>2021</risdate><abstract>We investigate in this work a fully-discrete semi-Lagrangian approximation of
second order possibly degenerate Hamilton-Jacobi-Bellman (HJB) equations on a
bounded domain with oblique boundary conditions. These equations appear
naturally in the study of optimal control of diffusion processes with oblique
reflection at the boundary of the domain.
The proposed scheme is shown to satisfy a consistency type property, it is
monotone and stable. Our main result is the convergence of the numerical
solution towards the unique viscosity solution of the HJB equation. The
convergence result holds under the same asymptotic relation between the time
and space discretization steps as in the classical setting for semi-Lagrangian
schemes. We present some numerical results that confirm the numerical
convergence of the scheme.</abstract><doi>10.48550/arxiv.2109.10228</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Numerical Analysis Mathematics - Numerical Analysis |
| title | A semi-Lagrangian scheme for Hamilton-Jacobi-Bellman equations with oblique boundary conditions |
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