{"id":"https://openalex.org/W2083411653","doi":"https://doi.org/10.1007/s10107-015-0874-5","title":"A Lagrangian\u2013DNN relaxation: a fast method for computing tight lower bounds for a class of quadratic optimization problems","display_name":"A Lagrangian\u2013DNN relaxation: a fast method for computing tight lower bounds for a class of quadratic optimization problems","publication_year":2015,"publication_date":"2015-02-20","ids":{"openalex":"https://openalex.org/W2083411653","doi":"https://doi.org/10.1007/s10107-015-0874-5","mag":"2083411653"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-015-0874-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-015-0874-5","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100333111","display_name":"Sunyoung Kim","orcid":"https://orcid.org/0000-0003-3705-9746"},"institutions":[{"id":"https://openalex.org/I138925566","display_name":"Ewha Womans University","ror":"https://ror.org/053fp5c05","country_code":"KR","type":"education","lineage":["https://openalex.org/I138925566"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Sunyoung Kim","raw_affiliation_strings":["Department of Mathematics, Ewha W. University, 52 Ewhayeodae-gil, Sudaemoon-gu, Seoul, 120-750, Korea","Department of Mathematics, Ewha W. University, Seoul, Korea 120-750"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ewha W. University, 52 Ewhayeodae-gil, Sudaemoon-gu, Seoul, 120-750, Korea","institution_ids":["https://openalex.org/I138925566"]},{"raw_affiliation_string":"Department of Mathematics, Ewha W. University, Seoul, Korea 120-750","institution_ids":["https://openalex.org/I138925566"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113974670","display_name":"Masakazu Kojima","orcid":null},"institutions":[{"id":"https://openalex.org/I96679780","display_name":"Chuo University","ror":"https://ror.org/03qvqb743","country_code":"JP","type":"education","lineage":["https://openalex.org/I96679780"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masakazu Kojima","raw_affiliation_strings":["Research and Development Initiative, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan","Research and Development Initiative, Chuo University, Tokyo, Japan 112-8551"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research and Development Initiative, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan","institution_ids":["https://openalex.org/I96679780"]},{"raw_affiliation_string":"Research and Development Initiative, Chuo University, Tokyo, Japan 112-8551","institution_ids":["https://openalex.org/I96679780"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064083862","display_name":"Kim-Chuan Toh","orcid":"https://orcid.org/0000-0001-7204-8933"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Kim-Chuan Toh","raw_affiliation_strings":["Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore, 119076, Singapore","Department of Mathematics, National University of Singapore, Singapore, Singapore 119076#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore, 119076, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"Department of Mathematics, National University of Singapore, Singapore, Singapore 119076#TAB#","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100333111"],"corresponding_institution_ids":["https://openalex.org/I138925566"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":11.3782,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.99094818,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"156","issue":"1-2","first_page":"161","last_page":"187"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.996999979019165,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9847999811172485,"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/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.84312903881073},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7733972072601318},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.7139544486999512},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.7107760906219482},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5315282940864563},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49596652388572693},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4949747920036316},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4854510426521301},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4397532343864441},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07902792096138}],"concepts":[{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.84312903881073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7733972072601318},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.7139544486999512},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.7107760906219482},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5315282940864563},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49596652388572693},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4949747920036316},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4854510426521301},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4397532343864441},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07902792096138},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-015-0874-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-015-0874-5","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:CiteSeerX.psu:10.1.1.698.4774","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.698.4774","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.nus.edu.sg/%7Emattohkc/papers/KKT.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7546307418","display_name":"Research and Development of Decision Making Platform by New Optimization Model","funder_award_id":"26242027","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1632601927","https://openalex.org/W1730217376","https://openalex.org/W1864272955","https://openalex.org/W1964730816","https://openalex.org/W1967073510","https://openalex.org/W1985181089","https://openalex.org/W1987255230","https://openalex.org/W1992841740","https://openalex.org/W1999613943","https://openalex.org/W1999913571","https://openalex.org/W2020570543","https://openalex.org/W2028570814","https://openalex.org/W2033498477","https://openalex.org/W2045079045","https://openalex.org/W2056145308","https://openalex.org/W2061830070","https://openalex.org/W2078600458","https://openalex.org/W2079135578","https://openalex.org/W2099799470","https://openalex.org/W2100556411","https://openalex.org/W2107888388","https://openalex.org/W2120146316","https://openalex.org/W2142333440","https://openalex.org/W2144560699","https://openalex.org/W2158226611","https://openalex.org/W2169053534","https://openalex.org/W2186191937","https://openalex.org/W2244987555","https://openalex.org/W2280348062","https://openalex.org/W2285258089","https://openalex.org/W2473029355","https://openalex.org/W2566293603","https://openalex.org/W2798766386","https://openalex.org/W3086232072","https://openalex.org/W3111467837","https://openalex.org/W4242209908","https://openalex.org/W4256141204","https://openalex.org/W6603251197","https://openalex.org/W6725080867"],"related_works":["https://openalex.org/W2002102264","https://openalex.org/W2015060724","https://openalex.org/W2058578573","https://openalex.org/W3105202832","https://openalex.org/W2360271985","https://openalex.org/W4237964977","https://openalex.org/W2012871340","https://openalex.org/W3046535663","https://openalex.org/W1996993548","https://openalex.org/W3207854495"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
