{"id":"https://openalex.org/W4225161449","doi":"https://doi.org/10.1007/s10851-022-01089-9","title":"On Convergence of the Arrow\u2013Hurwicz Method for Saddle Point Problems","display_name":"On Convergence of the Arrow\u2013Hurwicz Method for Saddle Point Problems","publication_year":2022,"publication_date":"2022-04-29","ids":{"openalex":"https://openalex.org/W4225161449","doi":"https://doi.org/10.1007/s10851-022-01089-9"},"language":"en","primary_location":{"id":"doi:10.1007/s10851-022-01089-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10851-022-01089-9","pdf_url":null,"source":{"id":"https://openalex.org/S66221708","display_name":"Journal of Mathematical Imaging and Vision","issn_l":"0924-9907","issn":["0924-9907","1573-7683"],"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":"Journal of Mathematical Imaging and Vision","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/A5039946576","display_name":"Bingsheng He","orcid":"https://orcid.org/0000-0001-8618-4581"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bingsheng He","raw_affiliation_strings":["Department of Mathematics, Nanjing University, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024969203","display_name":"Shengjie Xu","orcid":"https://orcid.org/0000-0003-2019-5186"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I3045169105","display_name":"Southern University of Science and Technology","ror":"https://ror.org/049tv2d57","country_code":"CN","type":"education","lineage":["https://openalex.org/I3045169105"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shengjie Xu","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology, Harbin, China","Department of Mathematics, Southern University of Science and Technology, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mathematics, Southern University of Science and Technology, Shenzhen, China","institution_ids":["https://openalex.org/I3045169105"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060269704","display_name":"Xiaoming Yuan","orcid":"https://orcid.org/0000-0002-6900-6983"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Xiaoming Yuan","raw_affiliation_strings":["Department of Mathematics, The University of Hong Kong, Pok Fu Lam, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Hong Kong, Pok Fu Lam, Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060269704"],"corresponding_institution_ids":["https://openalex.org/I889458895"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":1.6612,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.80092845,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"64","issue":"6","first_page":"662","last_page":"671"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987999796867371,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/saddle-point","display_name":"Saddle point","score":0.7256522178649902},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.621562659740448},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5618227124214172},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5547418594360352},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5530826449394226},{"id":"https://openalex.org/keywords/arrow","display_name":"Arrow","score":0.5315660834312439},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5139302611351013},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.44405218958854675},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.4218469560146332},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3702516555786133},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31541550159454346},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.08051320910453796},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06461280584335327}],"concepts":[{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.7256522178649902},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.621562659740448},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5618227124214172},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5547418594360352},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5530826449394226},{"id":"https://openalex.org/C2780339515","wikidata":"https://www.wikidata.org/wiki/Q3074698","display_name":"Arrow","level":2,"score":0.5315660834312439},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5139302611351013},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.44405218958854675},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.4218469560146332},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3702516555786133},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31541550159454346},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.08051320910453796},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06461280584335327},{"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},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10851-022-01089-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10851-022-01089-9","pdf_url":null,"source":{"id":"https://openalex.org/S66221708","display_name":"Journal of Mathematical Imaging and Vision","issn_l":"0924-9907","issn":["0924-9907","1573-7683"],"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":"Journal of Mathematical Imaging and Vision","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.46000000834465027,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G3129494189","display_name":null,"funder_award_id":"11871029","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4203296772","display_name":null,"funder_award_id":"12302318","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1968559856","https://openalex.org/W1973317191","https://openalex.org/W1981112674","https://openalex.org/W1985340647","https://openalex.org/W1988991628","https://openalex.org/W1993531186","https://openalex.org/W2004291775","https://openalex.org/W2016910236","https://openalex.org/W2021548137","https://openalex.org/W2057624533","https://openalex.org/W2073932184","https://openalex.org/W2075237894","https://openalex.org/W2092663520","https://openalex.org/W2094877794","https://openalex.org/W2103559027","https://openalex.org/W2141870784","https://openalex.org/W2158449358","https://openalex.org/W2241435520","https://openalex.org/W2405803404","https://openalex.org/W2491337109","https://openalex.org/W2510358906","https://openalex.org/W2523352299","https://openalex.org/W2589182068","https://openalex.org/W2964088716","https://openalex.org/W2988115680","https://openalex.org/W3016074254","https://openalex.org/W3023285721","https://openalex.org/W3100820186","https://openalex.org/W4210415421","https://openalex.org/W4291236916","https://openalex.org/W4292079189","https://openalex.org/W4296816584"],"related_works":["https://openalex.org/W4236459141","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W73248859","https://openalex.org/W2584253892","https://openalex.org/W2350324449","https://openalex.org/W119381072","https://openalex.org/W2034033896","https://openalex.org/W4240399920","https://openalex.org/W2901108086"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-17T18:11:37.981687","created_date":"2025-10-10T00:00:00"}