{"id":"https://openalex.org/W2019725228","doi":"https://doi.org/10.1007/bf01580904","title":"On the convergence of the affine-scaling algorithm","display_name":"On the convergence of the affine-scaling algorithm","publication_year":1992,"publication_date":"1992-08-01","ids":{"openalex":"https://openalex.org/W2019725228","doi":"https://doi.org/10.1007/bf01580904","mag":"2019725228"},"language":"en","primary_location":{"id":"doi:10.1007/bf01580904","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01580904","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":true,"oa_status":"green","oa_url":"https://dspace.mit.edu/bitstream/1721.1/3161/1/P-1920-20783110.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110258450","display_name":"Paul Tseng","orcid":null},"institutions":[{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Paul Tseng","raw_affiliation_strings":["Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA","Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]},{"raw_affiliation_string":"Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, USA#TAB#","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101766226","display_name":"Zhi\u2010Quan Luo","orcid":"https://orcid.org/0000-0003-3995-914X"},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Zhi-Quan Luo","raw_affiliation_strings":["Communications Research Laboratory, Department of Electrical and Computer Engineering, McMaster University, L8S 4L8, Hamilton, Ontario, Canada","Communications Research Laboratory, Department of Electrical and Computer Engineering, McMaster University, Hamilton, Canada"],"affiliations":[{"raw_affiliation_string":"Communications Research Laboratory, Department of Electrical and Computer Engineering, McMaster University, L8S 4L8, Hamilton, Ontario, Canada","institution_ids":["https://openalex.org/I98251732"]},{"raw_affiliation_string":"Communications Research Laboratory, Department of Electrical and Computer Engineering, McMaster University, Hamilton, Canada","institution_ids":["https://openalex.org/I98251732"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110258450"],"corresponding_institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":4.8416,"has_fulltext":true,"cited_by_count":41,"citation_normalized_percentile":{"value":0.94281377,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"56","issue":"1-3","first_page":"301","last_page":"319"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9987000226974487,"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/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":0.8189035654067993},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.7398953437805176},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.5978933572769165},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5503458976745605},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4660049378871918},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4581966996192932},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37780651450157166},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3549084961414337},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3540028929710388},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3283067047595978},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32135912775993347},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0734764039516449}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8189035654067993},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7398953437805176},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.5978933572769165},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5503458976745605},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4660049378871918},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4581966996192932},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37780651450157166},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3549084961414337},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3540028929710388},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3283067047595978},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32135912775993347},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0734764039516449},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/bf01580904","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01580904","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"},{"id":"pmh:oai:dspace.mit.edu:1721.1/3161","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/3161","pdf_url":"https://dspace.mit.edu/bitstream/1721.1/3161/1/P-1920-20783110.pdf","source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.94.7852","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.94.7852","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://dspace.mit.edu/bitstream/1721.1/3161/1/P-1920-20783110.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/3161","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/3161","pdf_url":"https://dspace.mit.edu/bitstream/1721.1/3161/1/P-1920-20783110.pdf","source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1266649876","display_name":"Computational Methods for Large-Scale Problems in Nonlinear Programming and Optimal Control","funder_award_id":"8519058","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7800732931","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320311526","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29"},{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2019725228.pdf","grobid_xml":"https://content.openalex.org/works/W2019725228.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W47264501","https://openalex.org/W615326371","https://openalex.org/W1528546869","https://openalex.org/W1603765807","https://openalex.org/W1964119857","https://openalex.org/W1973117121","https://openalex.org/W1974001978","https://openalex.org/W1992769584","https://openalex.org/W1993982015","https://openalex.org/W1998576973","https://openalex.org/W2002576214","https://openalex.org/W2004367844","https://openalex.org/W2011934229","https://openalex.org/W2024448501","https://openalex.org/W2026021734","https://openalex.org/W2030674458","https://openalex.org/W2039651888","https://openalex.org/W2049432961","https://openalex.org/W2053913299","https://openalex.org/W2057185554","https://openalex.org/W2061670230","https://openalex.org/W2066179689","https://openalex.org/W2069323107","https://openalex.org/W2086920040","https://openalex.org/W2090963365","https://openalex.org/W2094291659","https://openalex.org/W2108894884","https://openalex.org/W2116800096","https://openalex.org/W2119234846","https://openalex.org/W2146371908","https://openalex.org/W2155370486","https://openalex.org/W2165452678","https://openalex.org/W2168825111","https://openalex.org/W2334285086","https://openalex.org/W2599168675","https://openalex.org/W2611147814","https://openalex.org/W2922104599","https://openalex.org/W3140400264","https://openalex.org/W4235202054","https://openalex.org/W4285719527","https://openalex.org/W4299512035"],"related_works":["https://openalex.org/W2372940580","https://openalex.org/W2101113459","https://openalex.org/W2187706389","https://openalex.org/W2160348827","https://openalex.org/W1970824047","https://openalex.org/W1941883603","https://openalex.org/W1842556415","https://openalex.org/W4252688432","https://openalex.org/W1983011418","https://openalex.org/W1976246538"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}