{"id":"https://openalex.org/W2040779316","doi":"https://doi.org/10.1137/050632713","title":"Convergence of the Primal\u2010Dual Active Set Strategy for Diagonally Dominant Systems","display_name":"Convergence of the Primal\u2010Dual Active Set Strategy for Diagonally Dominant Systems","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2040779316","doi":"https://doi.org/10.1137/050632713","mag":"2040779316"},"language":"en","primary_location":{"id":"doi:10.1137/050632713","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050632713","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5004826461","display_name":"Kazufumi Ito","orcid":"https://orcid.org/0000-0003-2417-2600"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kazufumi Ito","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5074607617","display_name":"Karl Kunisch","orcid":"https://orcid.org/0000-0003-1113-7355"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karl Kunisch","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0177,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.76359393,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"46","issue":"1","first_page":"14","last_page":"34"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994000196456909,"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":0.9994000196456909,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9976999759674072,"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":0.9905999898910522,"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/mathematics","display_name":"Mathematics","score":0.834165632724762},{"id":"https://openalex.org/keywords/diagonally-dominant-matrix","display_name":"Diagonally dominant matrix","score":0.6582274436950684},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5641866326332092},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5254565477371216},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.512082576751709},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4664055407047272},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.4606618285179138},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4325324296951294},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3724842667579651},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16635984182357788}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.834165632724762},{"id":"https://openalex.org/C84507854","wikidata":"https://www.wikidata.org/wiki/Q952222","display_name":"Diagonally dominant matrix","level":3,"score":0.6582274436950684},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5641866326332092},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5254565477371216},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.512082576751709},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4664055407047272},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4606618285179138},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4325324296951294},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3724842667579651},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16635984182357788},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050632713","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050632713","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6499999761581421}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1545571671","https://openalex.org/W1551360398","https://openalex.org/W2026365342","https://openalex.org/W2076887500","https://openalex.org/W2135978105","https://openalex.org/W2171467378","https://openalex.org/W4234200150","https://openalex.org/W4250028192"],"related_works":["https://openalex.org/W2367535589","https://openalex.org/W2348298710","https://openalex.org/W1976521968","https://openalex.org/W2013133372","https://openalex.org/W2136336099","https://openalex.org/W2550293690","https://openalex.org/W1529195008","https://openalex.org/W2357224165","https://openalex.org/W2238553753","https://openalex.org/W2139574475"],"abstract_inverted_index":{"Sufficient":[0],"conditions":[1,32,55],"for":[2,11,56],"global":[3],"convergence":[4],"of":[5,40],"the":[6,41,44,57],"primal\u2010dual":[7,58],"active":[8,59],"set":[9,60],"strategy":[10],"finite":[12],"and":[13,26,36,52],"infinite":[14],"dimensional":[15],"quadratic,":[16],"as":[17,19],"well":[18],"nonlinear":[20],"optimization,":[21],"problems":[22],"with":[23],"affine":[24],"equality":[25],"inequality":[27],"constraints":[28],"are":[29,49,67],"presented.":[30],"These":[31],"involve":[33],"diagonal":[34],"dominance":[35],"cone":[37],"preserving":[38],"properties":[39],"operator":[42],"defining":[43],"cost":[45],"functional.":[46],"Globalization":[47],"strategies":[48],"also":[50],"provided,":[51],"specific":[53],"sufficient":[54],"step":[61],"to":[62],"have":[63],"a":[64],"descent":[65],"property":[66],"given.":[68]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}