{"id":"https://openalex.org/W2962885385","doi":"https://doi.org/10.1007/s10589-019-00102-z","title":"Quasi-Newton approaches to interior point methods for quadratic problems","display_name":"Quasi-Newton approaches to interior point methods for quadratic problems","publication_year":2019,"publication_date":"2019-05-02","ids":{"openalex":"https://openalex.org/W2962885385","doi":"https://doi.org/10.1007/s10589-019-00102-z","mag":"2962885385"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-019-00102-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-019-00102-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-019-00102-z.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10589-019-00102-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033855320","display_name":"Jacek Gondzio","orcid":"https://orcid.org/0000-0002-6270-4666"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"J. Gondzio","raw_affiliation_strings":["School of Mathematics, University of Edinburgh, Edinburgh, EH9 3FD, Scotland, UK"],"raw_orcid":"https://orcid.org/0000-0002-6270-4666","affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Edinburgh, Edinburgh, EH9 3FD, Scotland, UK","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057295342","display_name":"F. N. C. Sobral","orcid":"https://orcid.org/0000-0003-4963-0946"},"institutions":[{"id":"https://openalex.org/I123443094","display_name":"Universidade Estadual de Maring\u00e1","ror":"https://ror.org/04bqqa360","country_code":"BR","type":"education","lineage":["https://openalex.org/I123443094"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"F. N. C. Sobral","raw_affiliation_strings":["Department of Mathematics, State University of Maring\u00e1, Avenida Colombo, 5790, Paran\u00e1, 87020-900, Brazil"],"raw_orcid":"https://orcid.org/0000-0003-4963-0946","affiliations":[{"raw_affiliation_string":"Department of Mathematics, State University of Maring\u00e1, Avenida Colombo, 5790, Paran\u00e1, 87020-900, Brazil","institution_ids":["https://openalex.org/I123443094"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5033855320"],"corresponding_institution_ids":["https://openalex.org/I98677209"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":2.9201,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.90869365,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"74","issue":"1","first_page":"93","last_page":"120"},"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/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/T11697","display_name":"Numerical Methods and Algorithms","score":0.995199978351593,"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/interior-point-method","display_name":"Interior point method","score":0.8140669465065002},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.7606072425842285},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.7153337001800537},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7026175260543823},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.546572208404541},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.545762836933136},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5427622199058533},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5378823280334473},{"id":"https://openalex.org/keywords/newtons-method-in-optimization","display_name":"Newton's method in optimization","score":0.49856996536254883},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.4891934394836426},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47701096534729004},{"id":"https://openalex.org/keywords/sequential-quadratic-programming","display_name":"Sequential quadratic programming","score":0.47200867533683777},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4131099283695221},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.39759117364883423},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.31333833932876587},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08151495456695557}],"concepts":[{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.8140669465065002},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.7606072425842285},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.7153337001800537},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7026175260543823},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.546572208404541},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.545762836933136},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5427622199058533},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5378823280334473},{"id":"https://openalex.org/C179127668","wikidata":"https://www.wikidata.org/wiki/Q17086396","display_name":"Newton's method in optimization","level":4,"score":0.49856996536254883},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.4891934394836426},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47701096534729004},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.47200867533683777},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4131099283695221},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.39759117364883423},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.31333833932876587},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08151495456695557},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10589-019-00102-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-019-00102-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-019-00102-z.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/29449065-a97c-40fc-b442-6d77838df328","is_oa":true,"landing_page_url":"https://hdl.handle.net/20.500.11820/29449065-a97c-40fc-b442-6d77838df328","pdf_url":"https://www.research.ed.ac.uk/files/82162970/qnIPM.pdf","source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","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":"Gondzio, J & Sobral, F N C 2019, 'Quasi-Newton approaches to Interior Point Methods for quadratic problems', Computational optimization and applications, vol. 74, no. 1, pp. 93-120. https://doi.org/10.1007/s10589-019-00102-z","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:RePEc:spr:coopap:v:74:y:2019:i:1:d:10.1007_s10589-019-00102-z","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10589-019-00102-z","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:pure.ed.ac.uk:publications/29449065-a97c-40fc-b442-6d77838df328","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/29449065-a97c-40fc-b442-6d77838df328","pdf_url":null,"source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"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":"Gondzio, J & Sobral, F N C 2019, 'Quasi-Newton approaches to Interior Point Methods for quadratic problems', Computational optimization and applications, vol. 74, no. 1, pp. 93-120. https://doi.org/10.1007/s10589-019-00102-z","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s10589-019-00102-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-019-00102-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-019-00102-z.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320332","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2962885385.pdf","grobid_xml":"https://content.openalex.org/works/W2962885385.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W55017993","https://openalex.org/W1518039036","https://openalex.org/W1786620475","https://openalex.org/W1965651580","https://openalex.org/W1966323145","https://openalex.org/W1972015017","https://openalex.org/W2009926490","https://openalex.org/W2015130920","https://openalex.org/W2018238589","https://openalex.org/W2030356704","https://openalex.org/W2033477411","https://openalex.org/W2035814233","https://openalex.org/W2039400631","https://openalex.org/W2041563548","https://openalex.org/W2049219350","https://openalex.org/W2058696262","https://openalex.org/W2068484625","https://openalex.org/W2068531154","https://openalex.org/W2085548605","https://openalex.org/W2086867325","https://openalex.org/W2093911024","https://openalex.org/W2101154531","https://openalex.org/W2104414266","https://openalex.org/W2119287786","https://openalex.org/W2149454052","https://openalex.org/W2498939385","https://openalex.org/W2569942938","https://openalex.org/W2604122689","https://openalex.org/W2789543158","https://openalex.org/W3007791988","https://openalex.org/W3029645440","https://openalex.org/W4301014524"],"related_works":["https://openalex.org/W2044049628","https://openalex.org/W2082907018","https://openalex.org/W3001734434","https://openalex.org/W2131847826","https://openalex.org/W3048827262","https://openalex.org/W2075835091","https://openalex.org/W3206532668","https://openalex.org/W4289469101","https://openalex.org/W2731844756","https://openalex.org/W1513072274"],"abstract_inverted_index":{"Interior":[0],"point":[1,33,141],"methods":[2,109],"(IPM)":[3],"rely":[4],"on":[5],"the":[6,16,25,72,87,104,113,132,147,154],"Newton":[7,73],"method":[8,74],"for":[9,45,90,118],"solving":[10,47],"systems":[11,18],"of":[12,30,106,116,125,134,157],"nonlinear":[13,91,114],"equations.":[14],"Solving":[15],"linear":[17,48],"which":[19],"arise":[20],"from":[21],"this":[22,100],"approach":[23,149],"is":[24,66,150],"most":[26],"computationally":[27],"expensive":[28],"task":[29],"an":[31,96],"interior":[32,140],"iteration.":[34,142],"If,":[35],"due":[36],"to":[37,59,68,70,80,85,112,131,152],"problem\u2019s":[38],"inner":[39],"structure,":[40],"there":[41],"are":[42,57,83],"special":[43],"techniques":[44],"efficiently":[46],"systems,":[49],"IPMs":[50,81],"demonstrate":[51],"a":[52,138],"reduced":[53],"computing":[54,135],"time":[55],"and":[56],"able":[58,151],"solve":[60],"large":[61],"scale":[62],"optimization":[63],"problems.":[64,122],"It":[65],"tempting":[67],"try":[69],"replace":[71],"by":[75],"quasi-Newton":[76,108],"methods.":[77],"Quasi-Newton":[78],"approaches":[79],"either":[82],"built":[84],"approximate":[86],"Lagrangian":[88],"function":[89],"programming":[92,121],"problems":[93],"or":[94],"provide":[95],"inexpensive":[97],"preconditioner.":[98],"In":[99],"work":[101],"we":[102],"study":[103],"impact":[105],"using":[107],"applied":[110],"directly":[111],"system":[115],"equations":[117],"general":[119],"quadratic":[120],"The":[123],"cost":[124,133],"each":[126],"iteration":[127],"can":[128],"be":[129],"compared":[130],"correctors":[136],"in":[137],"usual":[139],"Numerical":[143],"experiments":[144],"show":[145],"that":[146],"new":[148],"reduce":[153],"overall":[155],"number":[156],"matrix":[158],"factorizations.":[159]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3}],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-10-10T00:00:00"}