{"id":"https://openalex.org/W1988778152","doi":"https://doi.org/10.1007/s10898-011-9765-3","title":"Exact penalty and error bounds in DC programming","display_name":"Exact penalty and error bounds in DC programming","publication_year":2011,"publication_date":"2011-09-23","ids":{"openalex":"https://openalex.org/W1988778152","doi":"https://doi.org/10.1007/s10898-011-9765-3","mag":"1988778152"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-011-9765-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-011-9765-3","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global Optimization","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/A5042936176","display_name":"Hoai An Le Thi","orcid":"https://orcid.org/0000-0002-2239-2100"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hoai An Le Thi","raw_affiliation_strings":["Laboratory of Theoretical and Applied Computer Science\u2014LITA EA 3097, UFR MIM, University of Paul Verlaine\u2014Metz, Ile du Saulcy, 57045, Metz, France","Laboratory of Theoretical and Applied Computer Science--LITA EA 3097, UFR MIM, University of Paul Verlaine--Metz, Ile du Saulcy, Metz, France 57045#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratory of Theoretical and Applied Computer Science\u2014LITA EA 3097, UFR MIM, University of Paul Verlaine\u2014Metz, Ile du Saulcy, 57045, Metz, France","institution_ids":[]},{"raw_affiliation_string":"Laboratory of Theoretical and Applied Computer Science--LITA EA 3097, UFR MIM, University of Paul Verlaine--Metz, Ile du Saulcy, Metz, France 57045#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112593835","display_name":"Tao Pham Dinh","orcid":null},"institutions":[{"id":"https://openalex.org/I196454796","display_name":"Institut National des Sciences Appliqu\u00e9es de Toulouse","ror":"https://ror.org/01h8pf755","country_code":"FR","type":"education","lineage":["https://openalex.org/I196454796","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I88814501","display_name":"Institut National des Sciences Appliqu\u00e9es Rouen Normandie","ror":"https://ror.org/020ws7586","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I88814501"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Tao Pham Dinh","raw_affiliation_strings":["LMI-National Institute for Applied Sciences-Rouen, BP08-Avenue de l\u2019Universit\u00e9, 76801, Saint-Etienne-du-Rouvray, France","LMI-National Institute for Applied Sciences-Rouen, Saint-Etienne-du-Rouvray, France 76801#TAB#"],"affiliations":[{"raw_affiliation_string":"LMI-National Institute for Applied Sciences-Rouen, BP08-Avenue de l\u2019Universit\u00e9, 76801, Saint-Etienne-du-Rouvray, France","institution_ids":["https://openalex.org/I88814501"]},{"raw_affiliation_string":"LMI-National Institute for Applied Sciences-Rouen, Saint-Etienne-du-Rouvray, France 76801#TAB#","institution_ids":["https://openalex.org/I88814501","https://openalex.org/I196454796"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103186037","display_name":"Huynh Van Ngai","orcid":"https://orcid.org/0000-0003-2040-7388"},"institutions":[{"id":"https://openalex.org/I4210137358","display_name":"Quy Nhon University","ror":"https://ror.org/04h4y6q56","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210137358"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Huynh Van Ngai","raw_affiliation_strings":["Department of Mathematics, University of Quynhon, 170 An Duong Vuong, Qui Nhon, Vietnam","Department of Mathematics, University of Quynhon, Qui Nhon, Vietnam#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Quynhon, 170 An Duong Vuong, Qui Nhon, Vietnam","institution_ids":["https://openalex.org/I4210137358"]},{"raw_affiliation_string":"Department of Mathematics, University of Quynhon, Qui Nhon, Vietnam#TAB#","institution_ids":["https://openalex.org/I4210137358"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5042936176"],"corresponding_institution_ids":[],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":11.9262,"has_fulltext":false,"cited_by_count":173,"citation_normalized_percentile":{"value":0.99375941,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"52","issue":"3","first_page":"509","last_page":"535"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"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":0.9993000030517578,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9979000091552734,"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/T12288","display_name":"Optimization and Search Problems","score":0.9947999715805054,"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/mathematics","display_name":"Mathematics","score":0.7791315317153931},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.6620218753814697},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6568377614021301},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5386881828308105},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1775335967540741},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.04205605387687683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7791315317153931},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.6620218753814697},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6568377614021301},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5386881828308105},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1775335967540741},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.04205605387687683}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10898-011-9765-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-011-9765-3","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01636730v1","is_oa":false,"landing_page_url":"https://hal.univ-lorraine.fr/hal-01636730","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Global Optimization, 2012, 52 (3), pp.509 - 535. &#x27E8;10.1007/s10898-011-9765-3&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-01664702v1","is_oa":false,"landing_page_url":"https://hal.univ-lorraine.fr/hal-01664702","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Vietnam Journal of Mathematics, 1999, 27 (2), pp.169-178. &#x27E8;10.1007/s10898-011-9765-3&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:RePEc:spr:jglopt:v:52:y:2012:i:3:p:509-535","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10898-011-9765-3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":[{"id":"https://metadata.un.org/sdg/10","score":0.5199999809265137,"display_name":"Reduced inequalities"},{"id":"https://metadata.un.org/sdg/16","score":0.4300000071525574,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":75,"referenced_works":["https://openalex.org/W75157487","https://openalex.org/W81332608","https://openalex.org/W81972919","https://openalex.org/W177396124","https://openalex.org/W202383464","https://openalex.org/W207658221","https://openalex.org/W639861265","https://openalex.org/W759920449","https://openalex.org/W1499399028","https://openalex.org/W1509448450","https://openalex.org/W1530146942","https://openalex.org/W1551360398","https://openalex.org/W1579203665","https://openalex.org/W1589133845","https://openalex.org/W1924300989","https://openalex.org/W1967114472","https://openalex.org/W1967213961","https://openalex.org/W1975852795","https://openalex.org/W1978320424","https://openalex.org/W1984174940","https://openalex.org/W1987228767","https://openalex.org/W1987314831","https://openalex.org/W1990310215","https://openalex.org/W1990494141","https://openalex.org/W1991607307","https://openalex.org/W1994196671","https://openalex.org/W1994229564","https://openalex.org/W1998360033","https://openalex.org/W2001598548","https://openalex.org/W2003383511","https://openalex.org/W2008195537","https://openalex.org/W2008832947","https://openalex.org/W2016019828","https://openalex.org/W2022083862","https://openalex.org/W2023452967","https://openalex.org/W2033604629","https://openalex.org/W2035321137","https://openalex.org/W2038323532","https://openalex.org/W2044297353","https://openalex.org/W2048312720","https://openalex.org/W2051664786","https://openalex.org/W2053428553","https://openalex.org/W2057932996","https://openalex.org/W2061907550","https://openalex.org/W2065119040","https://openalex.org/W2065139676","https://openalex.org/W2066651522","https://openalex.org/W2069369032","https://openalex.org/W2070606259","https://openalex.org/W2070791248","https://openalex.org/W2072058266","https://openalex.org/W2078721614","https://openalex.org/W2079424696","https://openalex.org/W2082451773","https://openalex.org/W2085563112","https://openalex.org/W2086234764","https://openalex.org/W2093035544","https://openalex.org/W2095929557","https://openalex.org/W2101292089","https://openalex.org/W2112395820","https://openalex.org/W2124768482","https://openalex.org/W2126827050","https://openalex.org/W2153562582","https://openalex.org/W2161737809","https://openalex.org/W2301746362","https://openalex.org/W2334285086","https://openalex.org/W2340859457","https://openalex.org/W2501231827","https://openalex.org/W3150183338","https://openalex.org/W3157341860","https://openalex.org/W4212864101","https://openalex.org/W4249667877","https://openalex.org/W4249840661","https://openalex.org/W4300987062","https://openalex.org/W4301056270"],"related_works":["https://openalex.org/W2018662469","https://openalex.org/W2109185638","https://openalex.org/W2098882706","https://openalex.org/W1988507758","https://openalex.org/W2048756781","https://openalex.org/W2347558389","https://openalex.org/W2106069570","https://openalex.org/W122341662","https://openalex.org/W4285154570","https://openalex.org/W2945790020"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":17},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":25},{"year":2018,"cited_by_count":19},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-07T14:57:38.498316","created_date":"2025-10-10T00:00:00"}
