{"id":"https://openalex.org/W2129264186","doi":"https://doi.org/10.1137/0805027","title":"Global Convergence of a Long-Step Affine Scaling Algorithm for Degenerate Linear Programming Problems","display_name":"Global Convergence of a Long-Step Affine Scaling Algorithm for Degenerate Linear Programming Problems","publication_year":1995,"publication_date":"1995-08-01","ids":{"openalex":"https://openalex.org/W2129264186","doi":"https://doi.org/10.1137/0805027","mag":"2129264186"},"language":"en","primary_location":{"id":"doi:10.1137/0805027","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0805027","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 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/A5020790231","display_name":"Takashi Tsuchiya","orcid":"https://orcid.org/0000-0002-6950-6160"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Takashi Tsuchiya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113934718","display_name":"Masakazu Muramatsu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Masakazu Muramatsu","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":15.6693,"has_fulltext":false,"cited_by_count":107,"citation_normalized_percentile":{"value":0.99517544,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"5","issue":"3","first_page":"525","last_page":"551"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9980999827384949,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980999827384949,"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":0.791144609451294},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.693423867225647},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.6203139424324036},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.5920406579971313},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5871874094009399},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5613134503364563},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5326153039932251},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.49770596623420715},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.47353050112724304},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4399992525577545},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4220958352088928},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4148615896701813},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4132891297340393},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40947282314300537},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19465649127960205},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12283524870872498},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11414220929145813},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08601260185241699}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.791144609451294},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.693423867225647},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.6203139424324036},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.5920406579971313},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5871874094009399},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5613134503364563},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5326153039932251},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.49770596623420715},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.47353050112724304},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4399992525577545},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4220958352088928},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4148615896701813},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4132891297340393},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40947282314300537},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19465649127960205},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12283524870872498},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11414220929145813},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08601260185241699},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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:10.1137/0805027","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0805027","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W631722187","https://openalex.org/W1533868172","https://openalex.org/W1573409602","https://openalex.org/W1966629740","https://openalex.org/W1973633794","https://openalex.org/W1976382569","https://openalex.org/W1981053712","https://openalex.org/W1986984076","https://openalex.org/W2002576214","https://openalex.org/W2019725228","https://openalex.org/W2025293484","https://openalex.org/W2026021734","https://openalex.org/W2030674458","https://openalex.org/W2045867632","https://openalex.org/W2049432961","https://openalex.org/W2057185554","https://openalex.org/W2059014132","https://openalex.org/W2074316151","https://openalex.org/W2086920040","https://openalex.org/W2094291659","https://openalex.org/W2116800096","https://openalex.org/W2146371908","https://openalex.org/W2154951198","https://openalex.org/W2165452678","https://openalex.org/W2611147814","https://openalex.org/W4233558979","https://openalex.org/W4251295118"],"related_works":["https://openalex.org/W2045867632","https://openalex.org/W2095983929","https://openalex.org/W211549749","https://openalex.org/W3205360536","https://openalex.org/W2165187848","https://openalex.org/W138441773","https://openalex.org/W1986648645","https://openalex.org/W4248698466","https://openalex.org/W4313348479","https://openalex.org/W2082565038"],"abstract_inverted_index":{"In":[0],"this":[1,133],"paper":[2],"we":[3,60],"present":[4],"new":[5],"global":[6],"convergence":[7,34,82,139],"results":[8],"on":[9,32,58],"a":[10,41,64],"long-step":[11,42],"affine":[12],"scaling":[13,44],"algorithm":[14,45],"obtained":[15],"by":[16,28],"means":[17],"of":[18,35,72,83,90,104,114,117,140,148],"the":[19,33,36,73,76,84,91,97,101,105,110,115,118,141,145,149],"local":[20],"Karmarkar":[21],"potential":[22],"functions.":[23],"This":[24],"development":[25],"was":[26],"triggered":[27],"Dikin\u2019s":[29],"interesting":[30],"result":[31,134],"dual":[37,98,106,142,150],"estimates":[38,99,143],"associated":[39],"with":[40,50],"afflne":[43],"for":[46],"homogeneous":[47],"LP":[48],"problems":[49],"unique":[51],"optimal":[52,92,107,151],"solutions.":[53],"Without":[54],"requiring":[55],"any":[56],"assumption":[57],"degeneracy,":[59],"show":[61],"that":[62,132],"moving":[63],"fixed":[65],"proportion":[66],"$\\lambda":[67],"$":[68],"up":[69],"to":[70,75,86,100,137,144],"two-thirds":[71],"way":[74],"boundary":[77],"at":[78],"each":[79],"iteration":[80],"ensures":[81],"iterates":[85],"an":[87,129],"interior":[88],"point":[89],"face":[93],"as":[94,96],"well":[95],"analytic":[102,146],"center":[103,147],"face,":[108],"where":[109],"asymptotic":[111],"reduction":[112],"rate":[113],"value":[116],"objective":[119],"function":[120],"is":[121,135],"$1":[122],"-":[123],"\\lambda":[124],"$.":[125],"We":[126],"also":[127],"give":[128],"example":[130],"showing":[131],"tight":[136],"obtain":[138],"face.":[152]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":34},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
