{"id":"https://openalex.org/W2148053278","doi":"https://doi.org/10.1137/040613718","title":"Solving Matrix Inequalities whose Unknowns are Matrices","display_name":"Solving Matrix Inequalities whose Unknowns are Matrices","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2148053278","doi":"https://doi.org/10.1137/040613718","mag":"2148053278"},"language":"en","primary_location":{"id":"doi:10.1137/040613718","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040613718","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://www.repositorio.unicamp.br/jspui/handle/REPOSIP/71872","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073743451","display_name":"Juan F. Camino","orcid":"https://orcid.org/0000-0002-9188-7166"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Juan F. Camino","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080005590","display_name":"J. William Helton","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. William Helton","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091183358","display_name":"Robert E. Skelton","orcid":"https://orcid.org/0000-0001-6503-9115"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert E. Skelton","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073743451"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6741,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.72697936,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"17","issue":"1","first_page":"1","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7334145307540894},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5819900035858154},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5024073123931885},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4883832335472107},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4802134931087494},{"id":"https://openalex.org/keywords/numerical-linear-algebra","display_name":"Numerical linear algebra","score":0.4629318118095398},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4607376456260681},{"id":"https://openalex.org/keywords/noncommutative-geometry","display_name":"Noncommutative geometry","score":0.41617900133132935},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38540923595428467},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.38231146335601807},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3481290340423584},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.34166744351387024},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15946340560913086},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09148326516151428}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7334145307540894},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5819900035858154},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5024073123931885},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4883832335472107},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4802134931087494},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.4629318118095398},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4607376456260681},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.41617900133132935},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38540923595428467},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.38231146335601807},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3481290340423584},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.34166744351387024},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15946340560913086},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09148326516151428},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/040613718","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040613718","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:repositorio.unicamp.br:REPOSIP/71872","is_oa":true,"landing_page_url":"http://www.repositorio.unicamp.br/jspui/handle/REPOSIP/71872","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Web of Science","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:americanae.aecid.es:2836665","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=2836665","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Web of Science","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:repositorio.unicamp.br:REPOSIP/71872","is_oa":true,"landing_page_url":"http://www.repositorio.unicamp.br/jspui/handle/REPOSIP/71872","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Web of Science","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5899999737739563,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W101469639","https://openalex.org/W1488435683","https://openalex.org/W1568064256","https://openalex.org/W1589786325","https://openalex.org/W1632601927","https://openalex.org/W1669462824","https://openalex.org/W1966069595","https://openalex.org/W1967073510","https://openalex.org/W1967969202","https://openalex.org/W1999913571","https://openalex.org/W2012110988","https://openalex.org/W2014746566","https://openalex.org/W2025883030","https://openalex.org/W2055241826","https://openalex.org/W2071425572","https://openalex.org/W2089024379","https://openalex.org/W2090963365","https://openalex.org/W2119080913","https://openalex.org/W2133404041","https://openalex.org/W2138135391","https://openalex.org/W2144787788","https://openalex.org/W2157590940","https://openalex.org/W2296319761","https://openalex.org/W2417903161","https://openalex.org/W2463908258","https://openalex.org/W2495457432","https://openalex.org/W2798909945","https://openalex.org/W4243539849","https://openalex.org/W4253016148"],"related_works":["https://openalex.org/W3111851529","https://openalex.org/W4210820417","https://openalex.org/W1592132747","https://openalex.org/W4252835080","https://openalex.org/W149575133","https://openalex.org/W4255270372","https://openalex.org/W1599993567","https://openalex.org/W4210382808","https://openalex.org/W1558217471","https://openalex.org/W2094769629"],"abstract_inverted_index":{"This":[0,19],"paper":[1],"provides":[2,79],"algorithms":[3,99],"for":[4,21,128],"numerical":[5,60,102],"solution":[6,88],"of":[7,34,47,67,115,124],"convex":[8],"matrix":[9,36,50,68,113],"inequalities":[10,37],"in":[11],"which":[12],"the":[13,48,87,112,116,118,122],"variables":[14],"naturally":[15],"appear":[16],"as":[17,41],"matrices.":[18],"includes,":[20],"instance,":[22],"many":[23,45],"systems":[24],"and":[25,71,103,106],"control":[26],"problems.":[27],"To":[28],"use":[29],"these":[30],"algorithms,":[31],"no":[32],"knowledge":[33],"linear":[35,49],"is":[38,91],"required.":[39],"However,":[40],"tools,":[42],"they":[43,108],"preserve":[44],"advantages":[46],"inequality":[51],"framework.":[52],"Our":[53],"method":[54],"has":[55],"two":[56],"components:":[57],"(1)":[58,90],"a":[59,64,73,80,92],"algorithm":[61],"that":[62,77,86,96],"solves":[63],"large":[65],"class":[66],"optimization":[69],"problems":[70],"(2)":[72],"symbolic":[74,105,119],"\"convexity":[75],"checker\"":[76],"automatically":[78],"region":[81],"which,":[82],"if":[83],"convex,":[84],"guarantees":[85],"from":[89],"global":[93],"optimum":[94],"on":[95],"region.":[97],"The":[98],"are":[100],"partly":[101,104],"since":[107],"aim":[109],"at":[110],"exploiting":[111],"structure":[114],"unknowns,":[117],"part":[120],"requires":[121],"development":[123],"new":[125],"computer":[126],"techniques":[127],"treating":[129],"noncommutative":[130],"algebra.":[131]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}