{"id":"https://openalex.org/W1986984076","doi":"https://doi.org/10.1007/bf02023109","title":"A simplified global convergence proof of the affine scaling algorithm","display_name":"A simplified global convergence proof of the affine scaling algorithm","publication_year":1993,"publication_date":"1993-09-01","ids":{"openalex":"https://openalex.org/W1986984076","doi":"https://doi.org/10.1007/bf02023109","mag":"1986984076"},"language":"en","primary_location":{"id":"doi:10.1007/bf02023109","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02023109","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":"Annals of Operations Research","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/A5108765688","display_name":"Renato D. C. Monteiro","orcid":null},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. D. C. Monteiro","raw_affiliation_strings":["[Department of Systems and Industrial Engineering, University of Arizona Tucson, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[Department of Systems and Industrial Engineering, University of Arizona Tucson, USA]","institution_ids":["https://openalex.org/I138006243"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020790231","display_name":"Takashi Tsuchiya","orcid":"https://orcid.org/0000-0002-6950-6160"},"institutions":[{"id":"https://openalex.org/I4210134673","display_name":"The Institute of Statistical Mathematics","ror":"https://ror.org/03jcejr58","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I4210134673","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"T. Tsuchiya","raw_affiliation_strings":["The Institute of Statistical Mathematics, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Institute of Statistical Mathematics, Tokyo, Japan","institution_ids":["https://openalex.org/I4210134673"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069169463","display_name":"Y. Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Y. Wang","raw_affiliation_strings":["[Department of Systems and Industrial Engineering, University of Arizona Tucson, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[Department of Systems and Industrial Engineering, University of Arizona Tucson, USA]","institution_ids":["https://openalex.org/I138006243"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":5.1783,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.96305542,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"46-47","issue":"2","first_page":"443","last_page":"482"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9983000159263611,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9939000010490417,"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/theory-of-computation","display_name":"Theory of computation","score":0.8247020840644836},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6878032684326172},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6211609840393066},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5849564671516418},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.520509660243988},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5098244547843933},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3828187882900238},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3399917483329773},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09577929973602295}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.8247020840644836},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6878032684326172},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6211609840393066},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5849564671516418},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.520509660243988},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5098244547843933},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3828187882900238},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3399917483329773},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09577929973602295},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02023109","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02023109","pdf_url":null,"source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"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":"Annals of Operations Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310133","display_name":"Rice University","ror":"https://ror.org/008zs3103"},{"id":"https://openalex.org/F4320310160","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1967960319","https://openalex.org/W1973633794","https://openalex.org/W1981053712","https://openalex.org/W2019725228","https://openalex.org/W2025293484","https://openalex.org/W2026021734","https://openalex.org/W2027552368","https://openalex.org/W2049432961","https://openalex.org/W2057185554","https://openalex.org/W2076680677","https://openalex.org/W2086920040","https://openalex.org/W2094291659","https://openalex.org/W2116800096","https://openalex.org/W2146371908","https://openalex.org/W2334285086","https://openalex.org/W2611147814","https://openalex.org/W4210281310","https://openalex.org/W4251295118"],"related_works":["https://openalex.org/W4378770497","https://openalex.org/W2049584446","https://openalex.org/W2079781215","https://openalex.org/W2064404759","https://openalex.org/W4385571583","https://openalex.org/W4308245303","https://openalex.org/W2910573937","https://openalex.org/W2014033564","https://openalex.org/W2034333739","https://openalex.org/W2368133486"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-23T13:55:30.953635","created_date":"2025-10-10T00:00:00"}
