{"id":"https://openalex.org/W4391021874","doi":"https://doi.org/10.1109/cdc49753.2023.10383232","title":"Multivariate Polynomial Optimization in Complex Variables Is a (Rectangular) Multiparameter Eigenvalue Problem","display_name":"Multivariate Polynomial Optimization in Complex Variables Is a (Rectangular) Multiparameter Eigenvalue Problem","publication_year":2023,"publication_date":"2023-12-13","ids":{"openalex":"https://openalex.org/W4391021874","doi":"https://doi.org/10.1109/cdc49753.2023.10383232"},"language":"en","primary_location":{"id":"doi:10.1109/cdc49753.2023.10383232","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/cdc49753.2023.10383232","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/retrieve/84d1d42e-6960-4d56-8df5-1b227d811deb","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008728823","display_name":"Christof Vermeersch","orcid":"https://orcid.org/0000-0003-1378-8952"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Christof Vermeersch","raw_affiliation_strings":["KU Leuven,Center for Dynamical Systems, Signal Processing, and Data Analytics (STADIUS),Dept. of Electrical Engineering (ESAT),Leuven,Belgium,3001"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KU Leuven,Center for Dynamical Systems, Signal Processing, and Data Analytics (STADIUS),Dept. of Electrical Engineering (ESAT),Leuven,Belgium,3001","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091947227","display_name":"Sibren Lagauw","orcid":"https://orcid.org/0000-0001-8130-1873"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Sibren Lagauw","raw_affiliation_strings":["KU Leuven,Center for Dynamical Systems, Signal Processing, and Data Analytics (STADIUS),Dept. of Electrical Engineering (ESAT),Leuven,Belgium,3001"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KU Leuven,Center for Dynamical Systems, Signal Processing, and Data Analytics (STADIUS),Dept. of Electrical Engineering (ESAT),Leuven,Belgium,3001","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018814006","display_name":"Bart De Moor","orcid":"https://orcid.org/0000-0002-1154-5028"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Bart De Moor","raw_affiliation_strings":["KU Leuven,Center for Dynamical Systems, Signal Processing, and Data Analytics (STADIUS),Dept. of Electrical Engineering (ESAT),Leuven,Belgium,3001"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KU Leuven,Center for Dynamical Systems, Signal Processing, and Data Analytics (STADIUS),Dept. of Electrical Engineering (ESAT),Leuven,Belgium,3001","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008728823"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27381845,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":null,"first_page":"7305","last_page":"7311"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"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":0.9993000030517578,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.996999979019165,"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/univariate","display_name":"Univariate","score":0.8025680780410767},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.7005031704902649},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.6799379587173462},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6686279773712158},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.657957911491394},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.6467680931091309},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6315762996673584},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5537407398223877},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5014026165008545},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4925695061683655},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.45807620882987976},{"id":"https://openalex.org/keywords/multivariable-calculus","display_name":"Multivariable calculus","score":0.41399508714675903},{"id":"https://openalex.org/keywords/complex-conjugate","display_name":"Complex conjugate","score":0.41309142112731934},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14364272356033325},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07715052366256714}],"concepts":[{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.8025680780410767},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.7005031704902649},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.6799379587173462},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6686279773712158},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.657957911491394},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.6467680931091309},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6315762996673584},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5537407398223877},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5014026165008545},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4925695061683655},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.45807620882987976},{"id":"https://openalex.org/C117312493","wikidata":"https://www.wikidata.org/wiki/Q2035437","display_name":"Multivariable calculus","level":2,"score":0.41399508714675903},{"id":"https://openalex.org/C45542137","wikidata":"https://www.wikidata.org/wiki/Q381040","display_name":"Complex conjugate","level":2,"score":0.41309142112731934},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14364272356033325},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07715052366256714},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cdc49753.2023.10383232","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/cdc49753.2023.10383232","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 62nd IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:20.500.12942/723793","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/723793","pdf_url":"https://lirias.kuleuven.be/retrieve/84d1d42e-6960-4d56-8df5-1b227d811deb","source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"6nd Conference on Decision and Control (CDC 2023), Singapore, 13-15 December 2023","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:lirias2repo.kuleuven.be:20.500.12942/736131","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/736131","pdf_url":"https://lirias.kuleuven.be/retrieve/34586945-eaa7-4f17-b171-cc9ee30b1779","source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"62nd Conference on Decision and Control (CDC), Marina Bay Sands, Singapore, 13-15 December 2023","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:20.500.12942/723793","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/723793","pdf_url":"https://lirias.kuleuven.be/retrieve/84d1d42e-6960-4d56-8df5-1b227d811deb","source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"6nd Conference on Decision and Control (CDC 2023), Singapore, 13-15 December 2023","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1214117848","display_name":null,"funder_award_id":"C24/18/022","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G1371775621","display_name":null,"funder_award_id":"C16/15/059","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G2115076930","display_name":null,"funder_award_id":"885682","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2493435547","display_name":null,"funder_award_id":"I013218N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G3167791836","display_name":null,"funder_award_id":"G0F6718N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G4466228027","display_name":null,"funder_award_id":"C3/20/117","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G4599083061","display_name":null,"funder_award_id":"HBC.2021.0076","funder_id":"https://openalex.org/F4320313460","funder_display_name":"Agentschap Innoveren en Ondernemen"},{"id":"https://openalex.org/G4707743599","display_name":null,"funder_award_id":"IOFm/16/004","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G5103706795","display_name":null,"funder_award_id":"C3/19/053","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G5109153945","display_name":null,"funder_award_id":"SB/1SA1319N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G7168511899","display_name":null,"funder_award_id":"1SA1319N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G7215814406","display_name":null,"funder_award_id":"T001919N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G7581210872","display_name":null,"funder_award_id":"C3I-21-00316","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G8407703196","display_name":null,"funder_award_id":"11K5623N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G894091104","display_name":null,"funder_award_id":"13-0260","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"}],"funders":[{"id":"https://openalex.org/F4320313460","display_name":"Agentschap Innoveren en Ondernemen","ror":"https://ror.org/032xdry56"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320322308","display_name":"KU Leuven","ror":"https://ror.org/05f950310"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4391021874.pdf","grobid_xml":"https://content.openalex.org/works/W4391021874.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W31443772","https://openalex.org/W179158423","https://openalex.org/W303777154","https://openalex.org/W404764422","https://openalex.org/W599332985","https://openalex.org/W1529743226","https://openalex.org/W1977574397","https://openalex.org/W2007088323","https://openalex.org/W2007715285","https://openalex.org/W2058693698","https://openalex.org/W2065234731","https://openalex.org/W2094995801","https://openalex.org/W2165281529","https://openalex.org/W2498144272","https://openalex.org/W2886036951","https://openalex.org/W2919677836","https://openalex.org/W3095095911","https://openalex.org/W3110348889","https://openalex.org/W3200539939","https://openalex.org/W4246425068","https://openalex.org/W4285247876","https://openalex.org/W4292096448","https://openalex.org/W4293775970","https://openalex.org/W4294862396","https://openalex.org/W6678738811"],"related_works":["https://openalex.org/W1489986405","https://openalex.org/W2382784327","https://openalex.org/W2140446896","https://openalex.org/W2335071938","https://openalex.org/W2023818677","https://openalex.org/W1973507931","https://openalex.org/W2905919007","https://openalex.org/W2086519601","https://openalex.org/W2357334848","https://openalex.org/W3004877956"],"abstract_inverted_index":{"We":[0,103],"extend":[1],"the":[2,13,18,28,47,71,76,88,94,98],"relation":[3],"between":[4],"univariate":[5],"polynomial":[6,14,30,44],"optimization":[7,31,109],"in":[8,46,65,80],"one":[9],"complex":[10,48,52,66,72],"variable":[11],"and":[12,50],"eigenvalue":[15,84],"problem":[16],"to":[17,60,93],"multivariate":[19,29,43],"case.":[20],"The":[21],"first-order":[22],"necessary":[23],"conditions":[24],"for":[25],"optimality":[26],"of":[27,42,70,90,97],"problem,":[32,85],"which":[33,91],"are":[34],"computed":[35],"using":[36],"Wirtinger":[37,54],"derivatives,":[38],"constitute":[39],"a":[40,81],"system":[41],"equations":[45],"variables":[49],"their":[51],"conjugates.":[53],"calculus":[55],"provides":[56],"an":[57],"elegant":[58],"way":[59],"differentiate":[61],"real-valued":[62,100],"(cost)":[63],"functions":[64],"variables.":[67],"An":[68],"elimination":[69],"conjugate":[73],"variables,":[74],"via":[75],"Macaulay":[77],"matrix,":[78],"results":[79],"(rectangular)":[82],"multiparameter":[83],"(some":[86],"of)":[87],"eigentuples":[89],"correspond":[92],"stationary":[95],"points":[96],"original":[99],"cost":[101],"function.":[102],"illustrate":[104],"our":[105],"novel":[106],"globally":[107],"optimal":[108],"approach":[110],"with":[111],"several":[112],"(didactical)":[113],"examples.":[114]},"counts_by_year":[],"updated_date":"2026-06-07T08:38:57.713557","created_date":"2025-10-10T00:00:00"}
