{"id":"https://openalex.org/W2073819859","doi":"https://doi.org/10.1016/0167-6377(96)00019-3","title":"Recovery of primal solutions when using subgradient optimization methods to solve Lagrangian duals of linear programs","display_name":"Recovery of primal solutions when using subgradient optimization methods to solve Lagrangian duals of linear programs","publication_year":1996,"publication_date":"1996-09-01","ids":{"openalex":"https://openalex.org/W2073819859","doi":"https://doi.org/10.1016/0167-6377(96)00019-3","mag":"2073819859"},"language":"en","primary_location":{"id":"doi:10.1016/0167-6377(96)00019-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0167-6377(96)00019-3","pdf_url":null,"source":{"id":"https://openalex.org/S27769002","display_name":"Operations Research Letters","issn_l":"0167-6377","issn":["0167-6377","1872-7468"],"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":"Operations Research Letters","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/A5043357545","display_name":"Hanif D. Sherali","orcid":null},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hanif D. Sherali","raw_affiliation_strings":["Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0118, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0118, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010716229","display_name":"Gyunghyun Choi","orcid":"https://orcid.org/0000-0002-6586-0525"},"institutions":[{"id":"https://openalex.org/I2250650973","display_name":"Samsung (South Korea)","ror":"https://ror.org/04w3jy968","country_code":"KR","type":"company","lineage":["https://openalex.org/I2250650973"]},{"id":"https://openalex.org/I4387155180","display_name":"Samsung SDS (South Korea)","ror":"https://ror.org/0476bn305","country_code":null,"type":"company","lineage":["https://openalex.org/I2250650973","https://openalex.org/I4387155180"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Gyunghyun Choi","raw_affiliation_strings":["SI Consulting Team, Samsung Data Systems, Imkwang Bldg. 219-1, Migun-Dong, Seodaemun-Gu, Seoul, South Korea 120-020","SI Consulting Team, Samsung Data Systems, Imkwang Bldg. 219-1, Migun-Dong, Seodaemun-Gu, Seoul, South Korea 120-020#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SI Consulting Team, Samsung Data Systems, Imkwang Bldg. 219-1, Migun-Dong, Seodaemun-Gu, Seoul, South Korea 120-020","institution_ids":["https://openalex.org/I2250650973","https://openalex.org/I4387155180"]},{"raw_affiliation_string":"SI Consulting Team, Samsung Data Systems, Imkwang Bldg. 219-1, Migun-Dong, Seodaemun-Gu, Seoul, South Korea 120-020#TAB#","institution_ids":["https://openalex.org/I2250650973","https://openalex.org/I4387155180"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5043357545"],"corresponding_institution_ids":["https://openalex.org/I859038795"],"apc_list":{"value":2760,"currency":"USD","value_usd":2760},"apc_paid":null,"fwci":2.288,"has_fulltext":false,"cited_by_count":178,"citation_normalized_percentile":{"value":0.88150719,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"19","issue":"3","first_page":"105","last_page":"113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9991000294685364,"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":0.9991000294685364,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"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/T12288","display_name":"Optimization and Search Problems","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/subgradient-method","display_name":"Subgradient method","score":0.9841684103012085},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.7825747132301331},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.7484530210494995},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.746953010559082},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.6152242422103882},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6150544285774231},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6119190454483032},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.5915884375572205},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.49337711930274963},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4736313223838806},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.4636384844779968},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4330364465713501},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.4265814423561096},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.39097416400909424},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3583011031150818},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33476442098617554},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.06200516223907471}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.9841684103012085},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.7825747132301331},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.7484530210494995},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.746953010559082},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.6152242422103882},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6150544285774231},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6119190454483032},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5915884375572205},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.49337711930274963},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4736313223838806},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.4636384844779968},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4330364465713501},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.4265814423561096},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.39097416400909424},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3583011031150818},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33476442098617554},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.06200516223907471},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0167-6377(96)00019-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0167-6377(96)00019-3","pdf_url":null,"source":{"id":"https://openalex.org/S27769002","display_name":"Operations Research Letters","issn_l":"0167-6377","issn":["0167-6377","1872-7468"],"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":"Operations Research Letters","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W224775207","https://openalex.org/W258481170","https://openalex.org/W1970720280","https://openalex.org/W1970750627","https://openalex.org/W1978797771","https://openalex.org/W2015127564","https://openalex.org/W2015263936","https://openalex.org/W2038295970","https://openalex.org/W2053300744","https://openalex.org/W2057560830","https://openalex.org/W2139211712","https://openalex.org/W2787523326","https://openalex.org/W2945904119","https://openalex.org/W4211092921","https://openalex.org/W4236384091","https://openalex.org/W6654079633","https://openalex.org/W6680517382"],"related_works":["https://openalex.org/W2037613239","https://openalex.org/W3183857959","https://openalex.org/W4243844638","https://openalex.org/W2894990380","https://openalex.org/W195910675","https://openalex.org/W3032916910","https://openalex.org/W2363143319","https://openalex.org/W2036724572","https://openalex.org/W2172478086","https://openalex.org/W2191696683"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":8},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":5}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
