{"id":"https://openalex.org/W2143075842","doi":"https://doi.org/10.1007/s10107-002-0352-8","title":"A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization","display_name":"A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization","publication_year":2003,"publication_date":"2003-02-01","ids":{"openalex":"https://openalex.org/W2143075842","doi":"https://doi.org/10.1007/s10107-002-0352-8","mag":"2143075842"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-002-0352-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-002-0352-8","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Samuel Burer","raw_affiliation_strings":["Department of Management Sciences, University of Iowa, Iowa City, IA 52242-1000, e-mail: burer@math.gatech.edu, , , , , , US","Department of Management Sciences, University of Iowa, Iowa City, IA 52242-1000, e-mail: burer@math.gatech.edu, , US"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Management Sciences, University of Iowa, Iowa City, IA 52242-1000, e-mail: burer@math.gatech.edu, , , , , , US","institution_ids":["https://openalex.org/I126307644"]},{"raw_affiliation_string":"Department of Management Sciences, University of Iowa, Iowa City, IA 52242-1000, e-mail: burer@math.gatech.edu, , US","institution_ids":["https://openalex.org/I126307644"]}]},{"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":["School of ISyE, Georgia Tech, Atlanta, GA 30332, USA,e-mail:monteiro@isye.gate, , , , , , US","School of ISyE, Georgia Tech, Atlanta, GA 30332, USA,e-mail:monteiro@isye.gate, , US"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of ISyE, Georgia Tech, Atlanta, GA 30332, USA,e-mail:monteiro@isye.gate, , , , , , US","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"School of ISyE, Georgia Tech, Atlanta, GA 30332, USA,e-mail:monteiro@isye.gate, , US","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":16.1117,"has_fulltext":false,"cited_by_count":835,"citation_normalized_percentile":{"value":0.99442074,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"95","issue":"2","first_page":"329","last_page":"357"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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":0.9998000264167786,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991999864578247,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9681000113487244,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.7646950483322144},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7407432198524475},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.7170422673225403},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.7015445232391357},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6053436994552612},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5824998617172241},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5377722978591919},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5360226035118103},{"id":"https://openalex.org/keywords/large-margin-nearest-neighbor","display_name":"Large margin nearest neighbor","score":0.521328866481781},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4950675070285797},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.4904730021953583},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.487179696559906},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4602448344230652},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4391126036643982},{"id":"https://openalex.org/keywords/trust-region","display_name":"Trust region","score":0.4185534715652466},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39952173829078674},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.216620534658432},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20068460702896118},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.19461342692375183},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.12717220187187195},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.09817948937416077},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07834190130233765}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7646950483322144},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7407432198524475},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.7170422673225403},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.7015445232391357},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6053436994552612},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5824998617172241},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5377722978591919},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5360226035118103},{"id":"https://openalex.org/C94475309","wikidata":"https://www.wikidata.org/wiki/Q6489154","display_name":"Large margin nearest neighbor","level":3,"score":0.521328866481781},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4950675070285797},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4904730021953583},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.487179696559906},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4602448344230652},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4391126036643982},{"id":"https://openalex.org/C89109886","wikidata":"https://www.wikidata.org/wiki/Q1535924","display_name":"Trust region","level":3,"score":0.4185534715652466},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39952173829078674},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.216620534658432},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20068460702896118},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.19461342692375183},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.12717220187187195},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.09817948937416077},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07834190130233765},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C116738811","wikidata":"https://www.wikidata.org/wiki/Q608751","display_name":"Nearest neighbor search","level":2,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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":5,"locations":[{"id":"doi:10.1007/s10107-002-0352-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-002-0352-8","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.27.2059","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.2059","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sburer.home.mindspring.com/paper8.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.27.3322","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.3322","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sburer.home.mindspring.com/paper8.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.682.1520","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.682.1520","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.optimization-online.org/DB_FILE/2001/03/296.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.89.8195","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.89.8195","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/007-lowrank.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1487348423","https://openalex.org/W1520493688","https://openalex.org/W1595045940","https://openalex.org/W1985123706","https://openalex.org/W2000602248","https://openalex.org/W2005102197","https://openalex.org/W2007068104","https://openalex.org/W2033852356","https://openalex.org/W2049371785","https://openalex.org/W2051306216","https://openalex.org/W2054776034","https://openalex.org/W2061607408","https://openalex.org/W2071143636","https://openalex.org/W2077658674","https://openalex.org/W2078289947","https://openalex.org/W2085595139","https://openalex.org/W2164948865","https://openalex.org/W2495457432","https://openalex.org/W2607539118","https://openalex.org/W2739590635","https://openalex.org/W2912522929","https://openalex.org/W3012317737","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2051421841","https://openalex.org/W2391916929","https://openalex.org/W2362452378","https://openalex.org/W2364528045","https://openalex.org/W2385886188","https://openalex.org/W2544939111","https://openalex.org/W2351113357","https://openalex.org/W2524928742","https://openalex.org/W2737505353","https://openalex.org/W2016506754"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":19},{"year":2025,"cited_by_count":50},{"year":2024,"cited_by_count":36},{"year":2023,"cited_by_count":38},{"year":2022,"cited_by_count":36},{"year":2021,"cited_by_count":79},{"year":2020,"cited_by_count":51},{"year":2019,"cited_by_count":66},{"year":2018,"cited_by_count":65},{"year":2017,"cited_by_count":55},{"year":2016,"cited_by_count":49},{"year":2015,"cited_by_count":40},{"year":2014,"cited_by_count":25},{"year":2013,"cited_by_count":30},{"year":2012,"cited_by_count":28}],"updated_date":"2026-08-02T14:50:37.381335","created_date":"2025-10-10T00:00:00"}
