{"id":"https://openalex.org/W1967365655","doi":"https://doi.org/10.1016/s0096-3003(02)00821-4","title":"The convergence of equilibrium algorithms with non-monotone line search technique","display_name":"The convergence of equilibrium algorithms with non-monotone line search technique","publication_year":2003,"publication_date":"2003-10-22","ids":{"openalex":"https://openalex.org/W1967365655","doi":"https://doi.org/10.1016/s0096-3003(02)00821-4","mag":"1967365655"},"language":"en","primary_location":{"id":"doi:10.1016/s0096-3003(02)00821-4","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(02)00821-4","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","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/A5049135480","display_name":"Ziyou Gao","orcid":"https://orcid.org/0000-0002-6519-4681"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ziyou Gao","raw_affiliation_strings":["School of Traffic and Transportation, Northern Jiaotong University, Beijing 100044, China","School of Traffic and Transportation,Northern Jiaotong University,Beijing 100044,China)"],"affiliations":[{"raw_affiliation_string":"School of Traffic and Transportation, Northern Jiaotong University, Beijing 100044, China","institution_ids":["https://openalex.org/I21193070"]},{"raw_affiliation_string":"School of Traffic and Transportation,Northern Jiaotong University,Beijing 100044,China)","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073956981","display_name":"William H. K. Lam","orcid":"https://orcid.org/0000-0002-7625-3712"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"W.H.K. Lam","raw_affiliation_strings":["Department of Civil Structure and Engineering, The Hong Kong Polytechnic University, Hong Kong, China","Department of Civil Structure and Engineering, The Hong Kong Polytechnic University, Hong Kong, China#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Civil Structure and Engineering, The Hong Kong Polytechnic University, Hong Kong, China","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Department of Civil Structure and Engineering, The Hong Kong Polytechnic University, Hong Kong, China#TAB#","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029977089","display_name":"S.C. Wong","orcid":"https://orcid.org/0000-0003-1169-7045"},"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":false,"raw_author_name":"S.C. Wong","raw_affiliation_strings":["Department of Civil Engineering, The University of Hong Kong, Hong Kong, China","(Department of Civil Engineering, The University of Hong Kong, Hong Kong, China)"],"affiliations":[{"raw_affiliation_string":"Department of Civil Engineering, The University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I889458895"]},{"raw_affiliation_string":"(Department of Civil Engineering, The University of Hong Kong, Hong Kong, China)","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045705475","display_name":"Hai Yang","orcid":"https://orcid.org/0000-0001-5210-8468"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"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":false,"raw_author_name":"H. Yang","raw_affiliation_strings":["Department of Civil Engineering, Hong Kong University of Science and Technology, Hong Kong, China","Department of Civil Engineering, Hong Kong University of Science & Technology, Hong Kong, China"],"affiliations":[{"raw_affiliation_string":"Department of Civil Engineering, Hong Kong University of Science and Technology, Hong Kong, China","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"Department of Civil Engineering, Hong Kong University of Science & Technology, Hong Kong, China","institution_ids":["https://openalex.org/I200769079","https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5049135480"],"corresponding_institution_ids":["https://openalex.org/I21193070"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.8681,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.71632653,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"148","issue":"1","first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9973000288009644,"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/T10698","display_name":"Transportation Planning and Optimization","score":0.972100019454956,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.7782675623893738},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6788546442985535},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6786918640136719},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6668087244033813},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.5730394124984741},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5592077374458313},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5177056789398193},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4963896870613098},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.49289846420288086},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.4517022669315338},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.45143020153045654},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38412603735923767},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2880668044090271},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.26515328884124756}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7782675623893738},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6788546442985535},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6786918640136719},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6668087244033813},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.5730394124984741},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5592077374458313},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5177056789398193},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4963896870613098},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.49289846420288086},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.4517022669315338},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.45143020153045654},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38412603735923767},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2880668044090271},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.26515328884124756},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/s0096-3003(02)00821-4","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(02)00821-4","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"},{"id":"pmh:oai:hub.hku.hk:10722/70720","is_oa":false,"landing_page_url":"http://hdl.handle.net/10722/70720","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/27346","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/27346","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-21717","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-21717","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321106","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W113519786","https://openalex.org/W117082138","https://openalex.org/W186009904","https://openalex.org/W1542473770","https://openalex.org/W1967942590","https://openalex.org/W1974058930","https://openalex.org/W1987161519","https://openalex.org/W1993721302","https://openalex.org/W1996952174","https://openalex.org/W2003912133","https://openalex.org/W2006122291","https://openalex.org/W2021431099","https://openalex.org/W2043430160","https://openalex.org/W2043851096","https://openalex.org/W2156920109","https://openalex.org/W2187576524","https://openalex.org/W4253922247"],"related_works":["https://openalex.org/W1516525943","https://openalex.org/W3135391181","https://openalex.org/W2094666307","https://openalex.org/W4361305142","https://openalex.org/W2784494936","https://openalex.org/W4387635768","https://openalex.org/W2376148546","https://openalex.org/W1883388834","https://openalex.org/W2361933918","https://openalex.org/W4288324104"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}
