{"id":"https://openalex.org/W2168204766","doi":"https://doi.org/10.1007/bf01585558","title":"A primal\u2014dual potential reduction method for problems involving matrix inequalities","display_name":"A primal\u2014dual potential reduction method for problems involving matrix inequalities","publication_year":1995,"publication_date":"1995-07-01","ids":{"openalex":"https://openalex.org/W2168204766","doi":"https://doi.org/10.1007/bf01585558","mag":"2168204766"},"language":"en","primary_location":{"id":"doi:10.1007/bf01585558","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01585558","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/A5017990990","display_name":"Lieven Vandenberghe","orcid":"https://orcid.org/0000-0003-4153-2268"},"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":"Lieven Vandenberghe","raw_affiliation_strings":["Departement Elektrotechniek, Afdeling ESAT, Katholieke Universiteit Leuven, K. Mercierlaan 94, 3001, Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departement Elektrotechniek, Afdeling ESAT, Katholieke Universiteit Leuven, K. Mercierlaan 94, 3001, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011176205","display_name":"Stephen Boyd","orcid":"https://orcid.org/0000-0001-8353-6000"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stephen Boyd","raw_affiliation_strings":["Information Systems Laboratory, Electrical Engineering Department, Stanford University, 94305, Stanford, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Systems Laboratory, Electrical Engineering Department, Stanford University, 94305, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017990990"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":35.7092,"has_fulltext":false,"cited_by_count":228,"citation_normalized_percentile":{"value":0.99955967,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"69","issue":"1-3","first_page":"205","last_page":"236"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9994999766349792,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987999796867371,"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":0.8047260642051697},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.7190150022506714},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.5742511749267578},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.566014289855957},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5551257729530334},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5219383239746094},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.49511995911598206},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4689606726169586},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4518331289291382},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4210035800933838},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4162459671497345},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4113454818725586},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3248552680015564},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.29004931449890137},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11372578144073486}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8047260642051697},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.7190150022506714},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.5742511749267578},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.566014289855957},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5551257729530334},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5219383239746094},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.49511995911598206},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4689606726169586},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4518331289291382},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4210035800933838},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4162459671497345},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4113454818725586},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3248552680015564},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.29004931449890137},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11372578144073486},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/bf01585558","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01585558","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:10.1.1.18.1281","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.1281","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.stanford.edu/~boyd/reports/pri_dual.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.367.7810","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.367.7810","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://stanford.edu/~boyd/papers/pdf/pd_pot_red.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.398.8541","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.398.8541","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://stanford.edu/~boyd/papers/pdf/pri_dual.pdf","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":32,"referenced_works":["https://openalex.org/W193768022","https://openalex.org/W1632601927","https://openalex.org/W1973207688","https://openalex.org/W1977532666","https://openalex.org/W1977705134","https://openalex.org/W1981053712","https://openalex.org/W1982604350","https://openalex.org/W1987953347","https://openalex.org/W1992975148","https://openalex.org/W1995195758","https://openalex.org/W1996267767","https://openalex.org/W2000630868","https://openalex.org/W2007179152","https://openalex.org/W2026287238","https://openalex.org/W2034235667","https://openalex.org/W2036622774","https://openalex.org/W2054689585","https://openalex.org/W2089024379","https://openalex.org/W2091964672","https://openalex.org/W2094326251","https://openalex.org/W2094757704","https://openalex.org/W2097897435","https://openalex.org/W2100440346","https://openalex.org/W2104431380","https://openalex.org/W2132248149","https://openalex.org/W2144787788","https://openalex.org/W2168825111","https://openalex.org/W2228687287","https://openalex.org/W2577865170","https://openalex.org/W2599168675","https://openalex.org/W2798909945","https://openalex.org/W3210839039"],"related_works":["https://openalex.org/W2036562274","https://openalex.org/W2121045497","https://openalex.org/W2269291726","https://openalex.org/W2965106131","https://openalex.org/W2239063252","https://openalex.org/W2114808974","https://openalex.org/W2128202699","https://openalex.org/W2531901171","https://openalex.org/W1985090152","https://openalex.org/W2617248812"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
