{"id":"https://openalex.org/W2007421997","doi":"https://doi.org/10.1007/s10107-006-0029-9","title":"On the solution of large-scale SDP problems by the modified barrier method using iterative solvers","display_name":"On the solution of large-scale SDP problems by the modified barrier method using iterative solvers","publication_year":2006,"publication_date":"2006-09-18","ids":{"openalex":"https://openalex.org/W2007421997","doi":"https://doi.org/10.1007/s10107-006-0029-9","mag":"2007421997"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-006-0029-9","doi":"https://doi.org/10.1007/s10107-006-0029-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-006-0029-9","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,"listed_in":["cwts-core","jufo-3","norway-2"],"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"},"volume":null,"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/A5041987187","display_name":"Michal Ko\u010dvara","orcid":"https://orcid.org/0000-0003-4414-0083","observed_orcids":["https://orcid.org/0000-0003-4414-0083"]},"institutions":[{"id":"https://openalex.org/I202391551","display_name":"Czech Academy of Sciences","ror":"https://ror.org/053avzc18","country_code":"CZ","type":"government","lineage":["https://openalex.org/I202391551"]},{"id":"https://openalex.org/I4210119419","display_name":"Czech Academy of Sciences, Institute of Information Theory and Automation","ror":"https://ror.org/03h1hsz49","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210119419"]},{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Michal Ko\u010dvara","raw_affiliation_strings":["Faculty of Electrical Engineering, Czech Technical University, Technick\u00e1 2, 166 27, Prague, Czech Republic","Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vod\u00e1renskou v\u011b\u017e\u00ed 4, 18208, Praha 8, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Electrical Engineering, Czech Technical University, Technick\u00e1 2, 166 27, Prague, Czech Republic","institution_ids":["https://openalex.org/I44504214"]},{"raw_affiliation_string":"Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vod\u00e1renskou v\u011b\u017e\u00ed 4, 18208, Praha 8, Czech Republic","institution_ids":["https://openalex.org/I202391551","https://openalex.org/I4210119419"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013459854","display_name":"Michael Stingl","orcid":"https://orcid.org/0000-0002-3626-0723","observed_orcids":["https://orcid.org/0000-0002-3626-0723"]},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael Stingl","raw_affiliation_strings":["Institute of Applied Mathematics, University of Erlangen, Martensstr. 3, 91058, Erlangen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, University of Erlangen, Martensstr. 3, 91058, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5041987187"],"corresponding_institution_ids":["https://openalex.org/I202391551","https://openalex.org/I4210119419","https://openalex.org/I44504214"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":7.5582,"has_fulltext":false,"cited_by_count":66,"citation_normalized_percentile":{"value":0.98259542,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"109","issue":"2-3","first_page":"413","last_page":"444"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9990000128746033,"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":0.9990000128746033,"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":0.0007999999797903001,"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/T10791","display_name":"Advanced Control Systems Optimization","score":9.999999747378752e-05,"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/semidefinite-programming","display_name":"semidefinite programming","score":0.9570000171661377},{"id":"https://openalex.org/keywords/large-scale-optimization","display_name":"large-scale optimization","score":0.8799999952316284},{"id":"https://openalex.org/keywords/iterative-solvers","display_name":"iterative solvers","score":0.843999981880188},{"id":"https://openalex.org/keywords/preconditioned-conjugate-gradient-method","display_name":"preconditioned conjugate gradient","score":0.9269999861717224},{"id":"https://openalex.org/keywords/memory-reduction","display_name":"memory reduction","score":0.49399998784065247},{"id":"https://openalex.org/keywords/finite-difference-approximation","display_name":"finite difference approximation","score":0.7670000195503235},{"id":"https://openalex.org/keywords/second-order-methods","display_name":"second-order methods","score":0.7379999756813049}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6882849335670471},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.6879559755325317},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.583249032497406},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5595887899398804},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5536832213401794},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.49075421690940857},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.47358113527297974},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.46503254771232605},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4584715962409973},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.450504332780838},{"id":"https://openalex.org/C134978465","wikidata":"https://www.wikidata.org/wiki/Q1654069","display_name":"Incomplete LU factorization","level":4,"score":0.42236900329589844},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.4179958701133728},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39797133207321167},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.3209909200668335},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2665949761867523},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.17031922936439514},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-006-0029-9","doi":"https://doi.org/10.1007/s10107-006-0029-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-006-0029-9","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,"listed_in":["cwts-core","jufo-3","norway-2"],"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:pure.atira.dk:openaire_cris_publications/9322808d-34ca-482f-ae6d-8009d3d3c17c","doi":null,"is_oa":false,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/9322808d-34ca-482f-ae6d-8009d3d3c17c","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Kocvara, M & Stingl, M 2007, 'On the solution of large-scale SDP problems by the modified barrier method using iterative solvers', Mathematical Programming, vol. 109, no. 2-3, pp. 413-444. https://doi.org/10.1007/s10107-006-0029-9","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1482750774","https://openalex.org/W1972015017","https://openalex.org/W1993000710","https://openalex.org/W2007157764","https://openalex.org/W2012110988","https://openalex.org/W2013621063","https://openalex.org/W2024457515","https://openalex.org/W2025486357","https://openalex.org/W2032229464","https://openalex.org/W2036562274","https://openalex.org/W2042360648","https://openalex.org/W2046866204","https://openalex.org/W2055102530","https://openalex.org/W2061607408","https://openalex.org/W2069572432","https://openalex.org/W2078190522","https://openalex.org/W2087228044","https://openalex.org/W2092162155","https://openalex.org/W2099799470","https://openalex.org/W2128202699","https://openalex.org/W2143075842","https://openalex.org/W2149454052","https://openalex.org/W2495390820","https://openalex.org/W3029645440"],"related_works":["https://openalex.org/W2129625121","https://openalex.org/W2375597358","https://openalex.org/W2356365850","https://openalex.org/W2383960336","https://openalex.org/W2353110519","https://openalex.org/W3159557833","https://openalex.org/W2352936229","https://openalex.org/W3159907817","https://openalex.org/W3123621400","https://openalex.org/W2369649360"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":7}],"updated_date":"2026-09-29T14:09:16.559479","created_date":"2025-10-10T00:00:00"}
