{"id":"https://openalex.org/W2094291659","doi":"https://doi.org/10.1007/bf01582896","title":"Global convergence of the affine scaling methods for degenerate linear programming problems","display_name":"Global convergence of the affine scaling methods for degenerate linear programming problems","publication_year":1991,"publication_date":"1991-05-01","ids":{"openalex":"https://openalex.org/W2094291659","doi":"https://doi.org/10.1007/bf01582896","mag":"2094291659"},"language":"en","primary_location":{"id":"doi:10.1007/bf01582896","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01582896","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/A5102836195","display_name":"Takashi Tsuchiya","orcid":"https://orcid.org/0000-0003-1878-9401"},"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":true,"raw_author_name":"Takashi Tsuchiya","raw_affiliation_strings":["The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106, Tokyo, Japan","The Institute of Statistical Mathematics, Tokyo, Japan 106#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106, Tokyo, Japan","institution_ids":["https://openalex.org/I4210134673"]},{"raw_affiliation_string":"The Institute of Statistical Mathematics, Tokyo, Japan 106#TAB#","institution_ids":["https://openalex.org/I4210134673"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102836195"],"corresponding_institution_ids":["https://openalex.org/I4210134673"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":6.02,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.97068584,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"52","issue":"1-3","first_page":"377","last_page":"404"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":1.0,"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":1.0,"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":0.9975000023841858,"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":0.9950000047683716,"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":0.831030011177063},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.7422505617141724},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.7378349900245667},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.643871545791626},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6042166948318481},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5999329090118408},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5564336776733398},{"id":"https://openalex.org/keywords/affine-combination","display_name":"Affine combination","score":0.5437501668930054},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.47110798954963684},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3760201334953308},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33817702531814575},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21285101771354675},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11460375785827637}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.831030011177063},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.7422505617141724},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7378349900245667},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.643871545791626},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6042166948318481},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5999329090118408},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5564336776733398},{"id":"https://openalex.org/C207221997","wikidata":"https://www.wikidata.org/wiki/Q938614","display_name":"Affine combination","level":3,"score":0.5437501668930054},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.47110798954963684},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3760201334953308},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33817702531814575},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21285101771354675},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11460375785827637},{"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/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01582896","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01582896","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322832","display_name":"University of Tokyo","ror":"https://ror.org/057zh3y96"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W631722187","https://openalex.org/W1963547452","https://openalex.org/W1967960319","https://openalex.org/W1981053712","https://openalex.org/W2002576214","https://openalex.org/W2019725228","https://openalex.org/W2026021734","https://openalex.org/W2049432961","https://openalex.org/W2057185554","https://openalex.org/W2059014132","https://openalex.org/W2086920040","https://openalex.org/W2116800096","https://openalex.org/W2146371908","https://openalex.org/W2154951198","https://openalex.org/W2611147814","https://openalex.org/W2971268466","https://openalex.org/W4301808069","https://openalex.org/W6655231430"],"related_works":["https://openalex.org/W2125277162","https://openalex.org/W1552514155","https://openalex.org/W4287687395","https://openalex.org/W2215112080","https://openalex.org/W3037733829","https://openalex.org/W2955288804","https://openalex.org/W4300428659","https://openalex.org/W2036979411","https://openalex.org/W168460013","https://openalex.org/W2026856841"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-23T13:55:30.953635","created_date":"2025-10-10T00:00:00"}