Numerical simulation of differential-algebraic equations with embedded global optimization criteria
We are considering differential-algebraic equations with embedded optimization criteria (DAEOs) in which the embedded optimization problem is solved by global optimization. This actually leads to differential inclusions for cases in which there are multiple global optimizer at the same time. Jump ev...
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| creator | Deussen, Jens Hüser, Jonathan Naumann, Uwe |
| description | We are considering differential-algebraic equations with embedded
optimization criteria (DAEOs) in which the embedded optimization problem is
solved by global optimization. This actually leads to differential inclusions
for cases in which there are multiple global optimizer at the same time. Jump
events from one global optimum to another result in nonsmooth DAEs and thus
reduction of the convergence order of the numerical integrator to first-order.
Implementation of event detection and location as introduced in this work
preserves the higher-order convergence behavior of the integrator. This allows
to compute discrete tangents and adjoint sensitivities for optimal control
problems. |
| doi_str_mv | 10.48550/arxiv.2305.05288 |
| format | Article |
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optimization criteria (DAEOs) in which the embedded optimization problem is
solved by global optimization. This actually leads to differential inclusions
for cases in which there are multiple global optimizer at the same time. Jump
events from one global optimum to another result in nonsmooth DAEs and thus
reduction of the convergence order of the numerical integrator to first-order.
Implementation of event detection and location as introduced in this work
preserves the higher-order convergence behavior of the integrator. This allows
to compute discrete tangents and adjoint sensitivities for optimal control
problems.</description><identifier>DOI: 10.48550/arxiv.2305.05288</identifier><language>eng</language><subject>Mathematics - Dynamical Systems ; Mathematics - Optimization and Control</subject><creationdate>2023-05</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/2305.05288$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2305.05288$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Deussen, Jens</creatorcontrib><creatorcontrib>Hüser, Jonathan</creatorcontrib><creatorcontrib>Naumann, Uwe</creatorcontrib><title>Numerical simulation of differential-algebraic equations with embedded global optimization criteria</title><description>We are considering differential-algebraic equations with embedded
optimization criteria (DAEOs) in which the embedded optimization problem is
solved by global optimization. This actually leads to differential inclusions
for cases in which there are multiple global optimizer at the same time. Jump
events from one global optimum to another result in nonsmooth DAEs and thus
reduction of the convergence order of the numerical integrator to first-order.
Implementation of event detection and location as introduced in this work
preserves the higher-order convergence behavior of the integrator. This allows
to compute discrete tangents and adjoint sensitivities for optimal control
problems.</description><subject>Mathematics - Dynamical Systems</subject><subject>Mathematics - Optimization and Control</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz7tOwzAUxnEvDKjwAEz4BRLs-BJnRBU3qYKle3RiH5cjOU1xEm5PT0k7fcunn_Rn7EaKUjtjxB3kb_osKyVMKUzl3CXzr3OPmTwkPlI_J5ho2PMh8kAxYsb9RJAKSDvsMpDn-DEvl5F_0fTOse8wBAx8l4buaAyHiXr6PSk-03S04YpdREgjXp93xbaPD9v1c7F5e3pZ328KsLUrsJFGh2ick9JDbWUjfeWVtihEpdAYUMEGa6zuTLA2am-bEOvovDYyNFGt2O2JXSrbQ6Ye8k_7X9suteoPAslR4g</recordid><startdate>20230509</startdate><enddate>20230509</enddate><creator>Deussen, Jens</creator><creator>Hüser, Jonathan</creator><creator>Naumann, Uwe</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230509</creationdate><title>Numerical simulation of differential-algebraic equations with embedded global optimization criteria</title><author>Deussen, Jens ; Hüser, Jonathan ; Naumann, Uwe</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a678-e9154df58811ca76191c2c346e0023e55a3d6d6564b5d66f4c69df7f8c451d9f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics - Dynamical Systems</topic><topic>Mathematics - Optimization and Control</topic><toplevel>online_resources</toplevel><creatorcontrib>Deussen, Jens</creatorcontrib><creatorcontrib>Hüser, Jonathan</creatorcontrib><creatorcontrib>Naumann, Uwe</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Deussen, Jens</au><au>Hüser, Jonathan</au><au>Naumann, Uwe</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical simulation of differential-algebraic equations with embedded global optimization criteria</atitle><date>2023-05-09</date><risdate>2023</risdate><abstract>We are considering differential-algebraic equations with embedded
optimization criteria (DAEOs) in which the embedded optimization problem is
solved by global optimization. This actually leads to differential inclusions
for cases in which there are multiple global optimizer at the same time. Jump
events from one global optimum to another result in nonsmooth DAEs and thus
reduction of the convergence order of the numerical integrator to first-order.
Implementation of event detection and location as introduced in this work
preserves the higher-order convergence behavior of the integrator. This allows
to compute discrete tangents and adjoint sensitivities for optimal control
problems.</abstract><doi>10.48550/arxiv.2305.05288</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Dynamical Systems Mathematics - Optimization and Control |
| title | Numerical simulation of differential-algebraic equations with embedded global optimization criteria |
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