{"id":"https://openalex.org/W2576448264","doi":"https://doi.org/10.1109/ecc.2016.7810576","title":"Sequential convex relaxation for convex optimization with bilinear matrix equalities","display_name":"Sequential convex relaxation for convex optimization with bilinear matrix equalities","publication_year":2016,"publication_date":"2016-06-01","ids":{"openalex":"https://openalex.org/W2576448264","doi":"https://doi.org/10.1109/ecc.2016.7810576","mag":"2576448264"},"language":"en","primary_location":{"id":"doi:10.1109/ecc.2016.7810576","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2016.7810576","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://resolver.tudelft.nl/uuid:0ef8bcbc-19e8-441c-834c-ef559d86683b","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058182093","display_name":"Reinier Doelman","orcid":"https://orcid.org/0000-0001-5986-627X"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Reinier Doelman","raw_affiliation_strings":["Delft University of Technology, Netherlands"],"affiliations":[{"raw_affiliation_string":"Delft University of Technology, Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003504954","display_name":"Michel Verhaegen","orcid":"https://orcid.org/0000-0002-7967-6884"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Michel Verhaegen","raw_affiliation_strings":["Delft University of Technology, Netherlands"],"affiliations":[{"raw_affiliation_string":"Delft University of Technology, Netherlands","institution_ids":["https://openalex.org/I98358874"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058182093"],"corresponding_institution_ids":["https://openalex.org/I98358874"],"apc_list":null,"apc_paid":null,"fwci":3.1146,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.91131547,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1946","last_page":"1951"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9980999827384949,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9948999881744385,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6832921504974365},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.6781450510025024},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.635168731212616},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5519242286682129},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5298207402229309},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5080959796905518},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.48398613929748535},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.46573084592819214},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4530285894870758},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.42682453989982605},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.4164675176143646},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.3558923006057739},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.34198498725891113},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2509450912475586},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2267291247844696},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.06998246908187866}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6832921504974365},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.6781450510025024},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.635168731212616},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5519242286682129},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5298207402229309},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5080959796905518},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.48398613929748535},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.46573084592819214},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4530285894870758},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.42682453989982605},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.4164675176143646},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.3558923006057739},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.34198498725891113},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2509450912475586},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2267291247844696},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.06998246908187866},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/ecc.2016.7810576","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2016.7810576","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 European Control Conference (ECC)","raw_type":"proceedings-article"},{"id":"pmh:tud:oai:tudelft.nl:uuid:0ef8bcbc-19e8-441c-834c-ef559d86683b","is_oa":true,"landing_page_url":"http://resolver.tudelft.nl/uuid:0ef8bcbc-19e8-441c-834c-ef559d86683b","pdf_url":"http://resolver.tudelft.nl/uuid:0ef8bcbc-19e8-441c-834c-ef559d86683b","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"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":"Proceedings 2016 European Control Conference (ECC 2016)","raw_type":"info:eu-repo/semantics/conferencepaper"}],"best_oa_location":{"id":"pmh:tud:oai:tudelft.nl:uuid:0ef8bcbc-19e8-441c-834c-ef559d86683b","is_oa":true,"landing_page_url":"http://resolver.tudelft.nl/uuid:0ef8bcbc-19e8-441c-834c-ef559d86683b","pdf_url":"http://resolver.tudelft.nl/uuid:0ef8bcbc-19e8-441c-834c-ef559d86683b","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"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":"Proceedings 2016 European Control Conference (ECC 2016)","raw_type":"info:eu-repo/semantics/conferencepaper"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6000000238418579,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2576448264.pdf","grobid_xml":"https://content.openalex.org/works/W2576448264.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1482934371","https://openalex.org/W1488475163","https://openalex.org/W1599634084","https://openalex.org/W1937324737","https://openalex.org/W1969698720","https://openalex.org/W1993446440","https://openalex.org/W1997867294","https://openalex.org/W2013621063","https://openalex.org/W2016696565","https://openalex.org/W2043363105","https://openalex.org/W2045548963","https://openalex.org/W2098954338","https://openalex.org/W2102461053","https://openalex.org/W2107028873","https://openalex.org/W2115424783","https://openalex.org/W2123556725","https://openalex.org/W2135904607","https://openalex.org/W2138578830","https://openalex.org/W2152731556","https://openalex.org/W2155420748","https://openalex.org/W2164904527","https://openalex.org/W2166765763","https://openalex.org/W2168550387","https://openalex.org/W2536620281","https://openalex.org/W6684557030"],"related_works":["https://openalex.org/W4381623700","https://openalex.org/W2020788389","https://openalex.org/W2317735557","https://openalex.org/W2126351339","https://openalex.org/W2388375429","https://openalex.org/W2147442790","https://openalex.org/W2379295215","https://openalex.org/W4728229","https://openalex.org/W2087726221","https://openalex.org/W2051968184"],"abstract_inverted_index":{"We":[0,75],"consider":[1],"the":[2,5,60,83,86,90,93],"use":[3],"of":[4,22,85,92],"nuclear":[6,65],"norm":[7,66,91],"operator,":[8],"and":[9,44,89],"its":[10],"tendency":[11],"to":[12,17,39,51,70],"produce":[13],"low":[14],"rank":[15,53,73],"results,":[16],"provide":[18,76],"a":[19,33,40,52,56,102],"convex":[20,64],"relaxation":[21],"Bilinear":[23],"Matrix":[24,35],"Inequalities":[25],"(BMIs).":[26],"The":[27,63,97],"BMI":[28],"is":[29,68,99],"first":[30],"written":[31],"as":[32],"Linear":[34],"Inequality":[36],"(LMI)":[37],"subject":[38,50],"bi-affine":[41],"equality":[42,94],"constraint":[43,54,95],"subsequently":[45],"rewritten":[46],"into":[47],"an":[48,77],"LMI":[49],"on":[55,82,101],"matrix":[57],"affine":[58],"in":[59],"decision":[61],"variables.":[62],"operator":[67],"used":[69],"relax":[71],"this":[72],"constraint.":[74],"algorithm":[78,98],"that":[79],"iteratively":[80],"improves":[81],"sum":[84],"objective":[87],"function":[88],"violation.":[96],"demonstrated":[100],"controller":[103],"synthesis":[104],"example.":[105]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}