{"id":"https://openalex.org/W2022429293","doi":"https://doi.org/10.1007/s10444-008-9097-0","title":"A dual algorithm for minimization of the LLT model","display_name":"A dual algorithm for minimization of the LLT model","publication_year":2008,"publication_date":"2008-08-19","ids":{"openalex":"https://openalex.org/W2022429293","doi":"https://doi.org/10.1007/s10444-008-9097-0","mag":"2022429293"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-008-9097-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-008-9097-0","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"Advances in Computational Mathematics","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/A5004592666","display_name":"Hua-zhu Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I173899330","display_name":"Henan University","ror":"https://ror.org/003xyzq10","country_code":"CN","type":"education","lineage":["https://openalex.org/I173899330"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hua-zhu Chen","raw_affiliation_strings":["College of Mathematics and Information Science, Henan University, Kaifeng, 475004, China","Institute of Mathematics, Henan University, Kaifeng, 475004, China","#N##TAB##TAB##TAB##TAB# Henan University#N##TAB##TAB##TAB#"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Henan University, Kaifeng, 475004, China","institution_ids":["https://openalex.org/I173899330"]},{"raw_affiliation_string":"Institute of Mathematics, Henan University, Kaifeng, 475004, China","institution_ids":["https://openalex.org/I173899330"]},{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# Henan University#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I173899330"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101096302","display_name":"Jinping Song","orcid":null},"institutions":[{"id":"https://openalex.org/I173899330","display_name":"Henan University","ror":"https://ror.org/003xyzq10","country_code":"CN","type":"education","lineage":["https://openalex.org/I173899330"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin-ping Song","raw_affiliation_strings":["College of Mathematics and Information Science, Henan University, Kaifeng, 475004, China","Institute of Mathematics, Henan University, Kaifeng, 475004, China","#N##TAB##TAB##TAB##TAB# Henan University#N##TAB##TAB##TAB#"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Henan University, Kaifeng, 475004, China","institution_ids":["https://openalex.org/I173899330"]},{"raw_affiliation_string":"Institute of Mathematics, Henan University, Kaifeng, 475004, China","institution_ids":["https://openalex.org/I173899330"]},{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# Henan University#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I173899330"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101951979","display_name":"Xue\u2010Cheng Tai","orcid":"https://orcid.org/0000-0003-3359-9104"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]},{"id":"https://openalex.org/I173899330","display_name":"Henan University","ror":"https://ror.org/003xyzq10","country_code":"CN","type":"education","lineage":["https://openalex.org/I173899330"]}],"countries":["CN","NO"],"is_corresponding":false,"raw_author_name":"Xue-Cheng Tai","raw_affiliation_strings":["College of Mathematics and Information Science, Henan University, Kaifeng, 475004, China","Department of Mathematics, University of Bergen, 5009, Bergen, Norway","University of Bergen","Henan University"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Henan University, Kaifeng, 475004, China","institution_ids":["https://openalex.org/I173899330"]},{"raw_affiliation_string":"Department of Mathematics, University of Bergen, 5009, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"University of Bergen","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"Henan University","institution_ids":["https://openalex.org/I173899330"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004592666"],"corresponding_institution_ids":["https://openalex.org/I173899330"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.2942,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.87693338,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"31","issue":"1-3","first_page":"115","last_page":"130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9896000027656555,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9896000027656555,"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/T10378","display_name":"Advanced MRI Techniques and Applications","score":0.98089998960495,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9800999760627747,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6909408569335938},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.6696758270263672},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6552149057388306},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6093214154243469},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6048355102539062},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.5706329941749573},{"id":"https://openalex.org/keywords/computational-science-and-engineering","display_name":"Computational Science and Engineering","score":0.55043625831604},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5350853800773621},{"id":"https://openalex.org/keywords/descent-direction","display_name":"Descent direction","score":0.4933880865573883},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4889942407608032},{"id":"https://openalex.org/keywords/ramer\u2013douglas\u2013peucker-algorithm","display_name":"Ramer\u2013Douglas\u2013Peucker algorithm","score":0.45136475563049316},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3806726336479187},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.29868370294570923},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2587040066719055},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15536147356033325},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.13945311307907104},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.10549044609069824},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.081534743309021}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6909408569335938},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.6696758270263672},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6552149057388306},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6093214154243469},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6048355102539062},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.5706329941749573},{"id":"https://openalex.org/C68597687","wikidata":"https://www.wikidata.org/wiki/Q362601","display_name":"Computational Science and Engineering","level":2,"score":0.55043625831604},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5350853800773621},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.4933880865573883},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4889942407608032},{"id":"https://openalex.org/C75930677","wikidata":"https://www.wikidata.org/wiki/Q1251950","display_name":"Ramer\u2013Douglas\u2013Peucker algorithm","level":3,"score":0.45136475563049316},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3806726336479187},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29868370294570923},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2587040066719055},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15536147356033325},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.13945311307907104},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.10549044609069824},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.081534743309021},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10444-008-9097-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-008-9097-0","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"Advances in Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322878","display_name":"Henan University","ror":"https://ror.org/003xyzq10"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1480353255","https://openalex.org/W1496099826","https://openalex.org/W1577281435","https://openalex.org/W1583497301","https://openalex.org/W1975919869","https://openalex.org/W1984213606","https://openalex.org/W1996898383","https://openalex.org/W2005089986","https://openalex.org/W2017848200","https://openalex.org/W2018237299","https://openalex.org/W2021504613","https://openalex.org/W2037981501","https://openalex.org/W2039939700","https://openalex.org/W2043153771","https://openalex.org/W2066630786","https://openalex.org/W2093109539","https://openalex.org/W2103559027","https://openalex.org/W2122287830","https://openalex.org/W2122890444","https://openalex.org/W2135036909","https://openalex.org/W2155267467","https://openalex.org/W2166129472","https://openalex.org/W2496526329","https://openalex.org/W3023249868"],"related_works":["https://openalex.org/W9059077","https://openalex.org/W2015288657","https://openalex.org/W39176023","https://openalex.org/W1985812215","https://openalex.org/W2111200844","https://openalex.org/W4389767465","https://openalex.org/W2054621035","https://openalex.org/W2381266720","https://openalex.org/W2046515352","https://openalex.org/W2484651380"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
