First-Order Algorithms for Constrained Nonlinear Dynamic Games
This paper presents algorithms for non-zero sum nonlinear constrained dynamic games with full information. Such problems emerge when multiple players with action constraints and differing objectives interact with the same dynamic system. They model a wide range of applications including economics, d...
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| creator | Di, Bolei Lamperski, Andrew |
| description | This paper presents algorithms for non-zero sum nonlinear constrained dynamic
games with full information. Such problems emerge when multiple players with
action constraints and differing objectives interact with the same dynamic
system. They model a wide range of applications including economics, defense,
and energy systems. We show how to exploit the temporal structure in projected
gradient and Douglas-Rachford (DR) splitting methods. The resulting algorithms
converge locally to open-loop Nash equilibria (OLNE) at linear rates.
Furthermore, we extend stagewise Newton method to find a local feedback policy
around an OLNE. In the of linear dynamics and polyhedral constraints, we show
that this local feedback controller is an approximated feedback Nash
equilibrium (FNE). Numerical examples are provided. |
| doi_str_mv | 10.48550/arxiv.2001.01826 |
| format | Article |
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games with full information. Such problems emerge when multiple players with
action constraints and differing objectives interact with the same dynamic
system. They model a wide range of applications including economics, defense,
and energy systems. We show how to exploit the temporal structure in projected
gradient and Douglas-Rachford (DR) splitting methods. The resulting algorithms
converge locally to open-loop Nash equilibria (OLNE) at linear rates.
Furthermore, we extend stagewise Newton method to find a local feedback policy
around an OLNE. In the of linear dynamics and polyhedral constraints, we show
that this local feedback controller is an approximated feedback Nash
equilibrium (FNE). Numerical examples are provided.</description><identifier>DOI: 10.48550/arxiv.2001.01826</identifier><language>eng</language><subject>Computer Science - Systems and Control</subject><creationdate>2020-01</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2001.01826$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2001.01826$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Di, Bolei</creatorcontrib><creatorcontrib>Lamperski, Andrew</creatorcontrib><title>First-Order Algorithms for Constrained Nonlinear Dynamic Games</title><description>This paper presents algorithms for non-zero sum nonlinear constrained dynamic
games with full information. Such problems emerge when multiple players with
action constraints and differing objectives interact with the same dynamic
system. They model a wide range of applications including economics, defense,
and energy systems. We show how to exploit the temporal structure in projected
gradient and Douglas-Rachford (DR) splitting methods. The resulting algorithms
converge locally to open-loop Nash equilibria (OLNE) at linear rates.
Furthermore, we extend stagewise Newton method to find a local feedback policy
around an OLNE. In the of linear dynamics and polyhedral constraints, we show
that this local feedback controller is an approximated feedback Nash
equilibrium (FNE). Numerical examples are provided.</description><subject>Computer Science - Systems and Control</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz71OwzAUhmEvDKhwAUz1DSS1fWLXWZCqQAtS1S7doxP_FEv5qY4jRO8eKEzfO33Sw9iTFGVltRYrpK_0WSohZCmkVeaePW8T5bk4kg_EN_15ojR_DJnHiXgzjXkmTGPw_DCN_U8g8ZfriENyfIdDyA_sLmKfw-P_Lthp-3pq3or9cffebPYFmrUpUHnQGgEBooOgo_Gxts5UtamslVrWSoIB40VUOgQrItSVcx3ITq9tF2DBln-3N0B7oTQgXdtfSHuDwDdGdUKE</recordid><startdate>20200106</startdate><enddate>20200106</enddate><creator>Di, Bolei</creator><creator>Lamperski, Andrew</creator><scope>AKY</scope><scope>GOX</scope></search><sort><creationdate>20200106</creationdate><title>First-Order Algorithms for Constrained Nonlinear Dynamic Games</title><author>Di, Bolei ; Lamperski, Andrew</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a676-a2d355a3a33fc3e5f6df98c64964881519213636d0f25ee80f394ccb31b578be3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Computer Science - Systems and Control</topic><toplevel>online_resources</toplevel><creatorcontrib>Di, Bolei</creatorcontrib><creatorcontrib>Lamperski, Andrew</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Di, Bolei</au><au>Lamperski, Andrew</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>First-Order Algorithms for Constrained Nonlinear Dynamic Games</atitle><date>2020-01-06</date><risdate>2020</risdate><abstract>This paper presents algorithms for non-zero sum nonlinear constrained dynamic
games with full information. Such problems emerge when multiple players with
action constraints and differing objectives interact with the same dynamic
system. They model a wide range of applications including economics, defense,
and energy systems. We show how to exploit the temporal structure in projected
gradient and Douglas-Rachford (DR) splitting methods. The resulting algorithms
converge locally to open-loop Nash equilibria (OLNE) at linear rates.
Furthermore, we extend stagewise Newton method to find a local feedback policy
around an OLNE. In the of linear dynamics and polyhedral constraints, we show
that this local feedback controller is an approximated feedback Nash
equilibrium (FNE). Numerical examples are provided.</abstract><doi>10.48550/arxiv.2001.01826</doi><oa>free_for_read</oa></addata></record> |
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| title | First-Order Algorithms for Constrained Nonlinear Dynamic Games |
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