{"id":"https://openalex.org/W4220834229","doi":"https://doi.org/10.3390/a15040121","title":"Combinatorial Integral Approximation Decompositions for Mixed-Integer Optimal Control","display_name":"Combinatorial Integral Approximation Decompositions for Mixed-Integer Optimal Control","publication_year":2022,"publication_date":"2022-03-31","ids":{"openalex":"https://openalex.org/W4220834229","doi":"https://doi.org/10.3390/a15040121"},"language":"en","primary_location":{"id":"doi:10.3390/a15040121","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15040121","pdf_url":"https://www.mdpi.com/1999-4893/15/4/121/pdf?version=1649330644","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/15/4/121/pdf?version=1649330644","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050928250","display_name":"Clemens Zeile","orcid":"https://orcid.org/0000-0003-3540-2897"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke University Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Clemens Zeile","raw_affiliation_strings":["Department of Mathematics, Otto-von-Guericke-Universit\u00e4t Magdeburg, 39106 Magdeburg, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Otto-von-Guericke-Universit\u00e4t Magdeburg, 39106 Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011294440","display_name":"Tobias Weber","orcid":"https://orcid.org/0000-0002-3015-3468"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke University Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tobias Weber","raw_affiliation_strings":["Department of Mathematics, Otto-von-Guericke-Universit\u00e4t Magdeburg, 39106 Magdeburg, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Otto-von-Guericke-Universit\u00e4t Magdeburg, 39106 Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070436541","display_name":"Sebastian S\u00e4ger","orcid":"https://orcid.org/0000-0002-0283-9075"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke University Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sebastian Sager","raw_affiliation_strings":["Department of Mathematics, Otto-von-Guericke-Universit\u00e4t Magdeburg, 39106 Magdeburg, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Otto-von-Guericke-Universit\u00e4t Magdeburg, 39106 Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050928250"],"corresponding_institution_ids":["https://openalex.org/I95793202"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.473,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.86965377,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"15","issue":"4","first_page":"121","last_page":"121"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6723659038543701},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6498739719390869},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5522310137748718},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5306253433227539},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4883977770805359},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4796769618988037},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3737376630306244},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23757335543632507}],"concepts":[{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6723659038543701},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6498739719390869},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5522310137748718},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5306253433227539},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4883977770805359},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4796769618988037},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3737376630306244},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23757335543632507},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a15040121","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15040121","pdf_url":"https://www.mdpi.com/1999-4893/15/4/121/pdf?version=1649330644","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3ba14e7030634e0bbcbacb57f3dc93d2","is_oa":true,"landing_page_url":"https://doaj.org/article/3ba14e7030634e0bbcbacb57f3dc93d2","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 15, Iss 4, p 121 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/15/4/121/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a15040121","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms; Volume 15; Issue 4; Pages: 121","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a15040121","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15040121","pdf_url":"https://www.mdpi.com/1999-4893/15/4/121/pdf?version=1649330644","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2626444877","display_name":null,"funder_award_id":"grant agreement No 647573)","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4220834229.pdf","grobid_xml":"https://content.openalex.org/works/W4220834229.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W603729728","https://openalex.org/W634094752","https://openalex.org/W636001447","https://openalex.org/W1514799972","https://openalex.org/W1570351331","https://openalex.org/W1973692576","https://openalex.org/W1980198193","https://openalex.org/W1987678257","https://openalex.org/W1990958757","https://openalex.org/W1994291732","https://openalex.org/W2021848705","https://openalex.org/W2027027181","https://openalex.org/W2035345497","https://openalex.org/W2041454172","https://openalex.org/W2049141170","https://openalex.org/W2053445302","https://openalex.org/W2059606830","https://openalex.org/W2089288642","https://openalex.org/W2089549742","https://openalex.org/W2092652152","https://openalex.org/W2094311908","https://openalex.org/W2099215853","https://openalex.org/W2099308299","https://openalex.org/W2107800111","https://openalex.org/W2133304166","https://openalex.org/W2141524119","https://openalex.org/W2147604579","https://openalex.org/W2162000525","https://openalex.org/W2258633420","https://openalex.org/W2391317397","https://openalex.org/W2403192619","https://openalex.org/W2514942416","https://openalex.org/W2583455981","https://openalex.org/W2790264739","https://openalex.org/W2948751856","https://openalex.org/W2953564759","https://openalex.org/W2963400379","https://openalex.org/W3015719863","https://openalex.org/W3027188463","https://openalex.org/W3038724928","https://openalex.org/W3093730648","https://openalex.org/W3100548955","https://openalex.org/W3105952231","https://openalex.org/W3112114392","https://openalex.org/W3155859492","https://openalex.org/W3163459486","https://openalex.org/W3165191782","https://openalex.org/W3174287382","https://openalex.org/W3177915143","https://openalex.org/W3200298776","https://openalex.org/W4220834229","https://openalex.org/W4235623249"],"related_works":["https://openalex.org/W4388311650","https://openalex.org/W5922282","https://openalex.org/W1974056099","https://openalex.org/W4245343541","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W62490179","https://openalex.org/W2954004777","https://openalex.org/W2951102138","https://openalex.org/W4298824844"],"abstract_inverted_index":{"Solving":[0],"mixed-integer":[1,56,84],"nonlinear":[2,16,79],"programs":[3],"(MINLPs)":[4],"is":[5,21,53],"hard":[6],"from":[7,23],"both":[8],"a":[9,24,68,74,112,148,182],"theoretical":[10],"and":[11,17,42,82,98,108,168,177,202],"practical":[12],"perspective.":[13],"Decomposing":[14],"the":[15,18,35,87,100,110,126,131,136,188,192],"integer":[19],"part":[20],"promising":[22,122],"computational":[25],"point":[26],"of":[27],"view.":[28],"In":[29,93],"general,":[30],"however,":[31],"no":[32],"bounds":[33,70],"on":[34],"objective":[36,199],"value":[37,201],"gap":[38],"can":[39],"be":[40],"established":[41],"iterative":[43],"procedures":[44],"with":[45,60,196,208],"potentially":[46],"many":[47],"subproblems":[48,178],"are":[49,145],"necessary.":[50],"The":[51],"situation":[52],"different":[54,106],"for":[55,73,125,138,156,161,164,169,181],"optimal":[57],"control":[58,80,128],"problems":[59],"binary":[61,127],"variables":[62],"that":[63],"switch":[64],"over":[65],"time.":[66],"Here,":[67],"priori":[69,113],"were":[71],"derived":[72],"decomposition":[75,101,195],"into":[76],"one":[77,83],"continuous":[78],"problem":[81],"linear":[85],"program,":[86],"combinatorial":[88,166],"integral":[89],"approximation":[90],"(CIA)":[91],"problem.":[92,133],"this":[94],"article,":[95],"we":[96,104,116],"generalize":[97],"extend":[99],"idea.":[102],"First,":[103],"derive":[105],"decompositions":[107],"analyze":[109],"implied":[111],"bounds.":[114],"Second,":[115],"propose":[117],"several":[118],"strategies":[119],"to":[120,152,191,198,204,210],"recombine":[121],"candidate":[123],"solutions":[124],"functions":[129],"in":[130,147,179],"original":[132],"We":[134,173],"present":[135],"extensions":[137,144],"ordinary":[139],"differential":[140,159],"equations-constrained":[141],"problems.":[142,172],"These":[143],"transferable":[146],"straightforward":[149],"way,":[150],"though,":[151],"recently":[153],"suggested":[154],"variants":[155],"certain":[157],"partial":[158],"equations,":[160,163],"algebraic":[162],"additional":[165],"constraints,":[167],"discrete":[170],"time":[171],"implemented":[174],"all":[175],"algorithms":[176],"AMPL":[180],"proof-of-concept":[183],"study.":[184],"Numerical":[185],"results":[186],"show":[187],"improvement":[189],"compared":[190,203],"standard":[193],"CIA":[194],"respect":[197,209],"function":[200],"general-purpose":[205],"MINLP":[206],"solvers":[207],"runtime.":[211]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}