{"id":"https://openalex.org/W1981344649","doi":"https://doi.org/10.1080/1055678031000111227","title":"A General Framework for Establishing Polynomial Convergence of Long-Step Methods for Semidefinite Programming","display_name":"A General Framework for Establishing Polynomial Convergence of Long-Step Methods for Semidefinite Programming","publication_year":2003,"publication_date":"2003-02-01","ids":{"openalex":"https://openalex.org/W1981344649","doi":"https://doi.org/10.1080/1055678031000111227","mag":"1981344649"},"language":"en","primary_location":{"id":"doi:10.1080/1055678031000111227","is_oa":false,"landing_page_url":"https://doi.org/10.1080/1055678031000111227","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002663715","display_name":"Samuel Burer","orcid":"https://orcid.org/0000-0001-5886-458X"},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]},{"id":"https://openalex.org/I4210155590","display_name":"Management Sciences (United States)","ror":"https://ror.org/05shz5j84","country_code":"US","type":"company","lineage":["https://openalex.org/I4210155590"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Samuel Burer","raw_affiliation_strings":["a    Department of Management Sciences, University of Iowa, Iowa City, Iowa 52242-1000, USA","Department of Management Sciences, University of Iowa, Iowa City, Iowa 52242-1000, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"a    Department of Management Sciences, University of Iowa, Iowa City, Iowa 52242-1000, USA","institution_ids":["https://openalex.org/I126307644"]},{"raw_affiliation_string":"Department of Management Sciences, University of Iowa, Iowa City, Iowa 52242-1000, USA","institution_ids":["https://openalex.org/I126307644","https://openalex.org/I4210155590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108765688","display_name":"Renato D. C. Monteiro","orcid":null},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Renato D.C. Monteiro","raw_affiliation_strings":["b    School of ISyE, Georgia Tech, Atlanta, Georgia 30332, USA","School of ISyE, Georgia Tech , Atlanta, Georgia, 30332, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"b    School of ISyE, Georgia Tech, Atlanta, Georgia 30332, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"School of ISyE, Georgia Tech , Atlanta, Georgia, 30332, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2461,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.77518871,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"1","first_page":"1","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9927999973297119,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9860000014305115,"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/mathematics","display_name":"Mathematics","score":0.7156693339347839},{"id":"https://openalex.org/keywords/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.6909013390541077},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.6848353147506714},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.6160436272621155},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.516128420829773},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4583780765533447},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4061289429664612},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3598523736000061},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.329656183719635},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.29965949058532715},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18316704034805298},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10917291045188904}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7156693339347839},{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.6909013390541077},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.6848353147506714},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6160436272621155},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.516128420829773},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4583780765533447},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4061289429664612},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3598523736000061},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.329656183719635},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29965949058532715},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18316704034805298},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10917291045188904},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/1055678031000111227","is_oa":false,"landing_page_url":"https://doi.org/10.1080/1055678031000111227","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.201.8348","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.201.8348","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dollar.biz.uiowa.edu/~burer/papers/002-longstepunify.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.44.4891","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.4891","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.isye.gatech.edu/~monteiro/tech_reports/unify.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1488435683","https://openalex.org/W1560108784","https://openalex.org/W1588330761","https://openalex.org/W1632601927","https://openalex.org/W1963753244","https://openalex.org/W1985984741","https://openalex.org/W1989395545","https://openalex.org/W1994350792","https://openalex.org/W1998493034","https://openalex.org/W2003324738","https://openalex.org/W2012110988","https://openalex.org/W2024899540","https://openalex.org/W2025486357","https://openalex.org/W2034235667","https://openalex.org/W2055592063","https://openalex.org/W2075379600","https://openalex.org/W2077274614","https://openalex.org/W2084622916","https://openalex.org/W2091044203","https://openalex.org/W2096247314","https://openalex.org/W2117065890","https://openalex.org/W2128202699","https://openalex.org/W2154089483","https://openalex.org/W2168204766"],"related_works":["https://openalex.org/W2504688771","https://openalex.org/W4255359805","https://openalex.org/W4315697090","https://openalex.org/W2002877864","https://openalex.org/W2394244817","https://openalex.org/W2075453197","https://openalex.org/W2924783966","https://openalex.org/W2233293187","https://openalex.org/W2770986973","https://openalex.org/W2057318281"],"abstract_inverted_index":{"This":[0],"article":[1],"considers":[2],"feasible":[3],"long-step":[4,53,87],"primal\u2013dual":[5],"path-following":[6],"methods":[7],"for":[8,51,86],"semidefinite":[9],"programming":[10],"based":[11,89],"on":[12,63,90],"Newton":[13],"directions":[14],"associated":[15],"with":[16],"central":[17],"path":[18],"equations":[19],"of":[20,59,68,72,77,112],"the":[21,36,40,52,69,91,108,117],"form":[22],"\u03a6":[23,38,97],"(PXP":[24],"T":[25],",":[26,95],"P":[27,43],"\u2212T":[28],"SP":[29],"\u22121)":[30],"\u2212":[31],"\u03bdI":[32],"=":[33,100,123],"0,":[34],"where":[35,105],"map":[37],"and":[39,96,114],"nonsingular":[41],"matrix":[42,120],"satisfy":[44],"several":[45],"key":[46],"properties.":[47],"An":[48],"iteration-complexity":[49,84],"bound":[50,62],"method":[54],"is":[55,107,116],"derived":[56],"in":[57],"terms":[58],"an":[60],"upper":[61],"a":[64,75],"certain":[65],"scaled":[66],"norm":[67],"second":[70],"derivative":[71],"\u03a6.":[73],"As":[74],"consequence":[76],"our":[78],"general":[79],"framework,":[80],"we":[81],"derive":[82],"polynomial":[83],"bounds":[85],"algorithms":[88],"following":[92],"four":[93],"maps:":[94],"(X,":[98],"S)":[99],"W":[101,115],"1/2":[102],"XSW":[103],"\u22121/2,":[104],"Lx":[106],"lower":[109],"Cholesky":[110],"factor":[111],"X":[113],"unique":[118],"symmetric":[119],"satisfying":[121],"S":[122],"WXW.":[124]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}