{"id":"https://openalex.org/W1974512477","doi":"https://doi.org/10.1007/s10898-011-9784-0","title":"Saddle point and exact penalty representation for generalized proximal Lagrangians","display_name":"Saddle point and exact penalty representation for generalized proximal Lagrangians","publication_year":2011,"publication_date":"2011-09-19","ids":{"openalex":"https://openalex.org/W1974512477","doi":"https://doi.org/10.1007/s10898-011-9784-0","mag":"1974512477"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-011-9784-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-011-9784-0","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/A5101475078","display_name":"Jinchuan Zhou","orcid":"https://orcid.org/0000-0002-2469-2123"},"institutions":[{"id":"https://openalex.org/I119203015","display_name":"Shandong University of Technology","ror":"https://ror.org/02mr3ar13","country_code":"CN","type":"education","lineage":["https://openalex.org/I119203015"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jinchuan Zhou","raw_affiliation_strings":["Department of Mathematics, School of Science, Shandong University of Technology, Zibo, 255049, People\u2019s Republic of China","SHANDONG UNIVERSITY OF TECHNOLOGY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, Shandong University of Technology, Zibo, 255049, People\u2019s Republic of China","institution_ids":["https://openalex.org/I119203015"]},{"raw_affiliation_string":"SHANDONG UNIVERSITY OF TECHNOLOGY","institution_ids":["https://openalex.org/I119203015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071551240","display_name":"Naihua Xiu","orcid":"https://orcid.org/0000-0002-3129-2005"},"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":false,"raw_author_name":"Naihua Xiu","raw_affiliation_strings":["Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, People\u2019s Republic of China","BeiJing Jiaotong Univ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, People\u2019s Republic of China","institution_ids":["https://openalex.org/I21193070"]},{"raw_affiliation_string":"BeiJing Jiaotong Univ","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100624270","display_name":"Changyu Wang","orcid":"https://orcid.org/0000-0001-8151-0480"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changyu Wang","raw_affiliation_strings":["Institute of Operations Research, Qufu Normal University, Qufu, 273165, People\u2019s Republic of China","Qufu Normal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Operations Research, Qufu Normal University, Qufu, 273165, People\u2019s Republic of China","institution_ids":["https://openalex.org/I202126657"]},{"raw_affiliation_string":"Qufu Normal University","institution_ids":["https://openalex.org/I202126657"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101475078"],"corresponding_institution_ids":["https://openalex.org/I119203015"],"apc_list":{"value":2780,"currency":"USD","value_usd":2780},"apc_paid":null,"fwci":0.4033,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.58331288,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"54","issue":"4","first_page":"669","last_page":"687"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9995999932289124,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9801999926567078,"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/saddle-point","display_name":"Saddle point","score":0.890691876411438},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8870925307273865},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.7533426284790039},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7375997304916382},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.6387798190116882},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.6186618804931641},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5610759854316711},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49505701661109924},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4741325378417969},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.46789443492889404},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4526127278804779},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44367504119873047},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.4283093214035034},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.101715087890625}],"concepts":[{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.890691876411438},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8870925307273865},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.7533426284790039},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7375997304916382},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6387798190116882},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.6186618804931641},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5610759854316711},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49505701661109924},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4741325378417969},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.46789443492889404},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4526127278804779},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44367504119873047},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4283093214035034},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.101715087890625},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10898-011-9784-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-011-9784-0","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:RePEc:spr:jglopt:v:54:y:2012:i:4:p:669-687","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10898-011-9784-0","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":[{"display_name":"Reduced inequalities","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W116715942","https://openalex.org/W258481170","https://openalex.org/W1514382660","https://openalex.org/W1531386198","https://openalex.org/W1669104078","https://openalex.org/W1966394100","https://openalex.org/W1974665512","https://openalex.org/W1986490170","https://openalex.org/W1989227105","https://openalex.org/W1997586153","https://openalex.org/W2026016914","https://openalex.org/W2037091587","https://openalex.org/W2038754896","https://openalex.org/W2042360648","https://openalex.org/W2052431132","https://openalex.org/W2057624533","https://openalex.org/W2062536941","https://openalex.org/W2076744267","https://openalex.org/W2092559257","https://openalex.org/W2119857700","https://openalex.org/W2123014493","https://openalex.org/W2133374626","https://openalex.org/W2141440245","https://openalex.org/W2167017375","https://openalex.org/W2266946488","https://openalex.org/W2787523326","https://openalex.org/W4249513058","https://openalex.org/W4285719527","https://openalex.org/W4291236916"],"related_works":["https://openalex.org/W4236459141","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W73248859","https://openalex.org/W2584253892","https://openalex.org/W2350324449","https://openalex.org/W1572705989","https://openalex.org/W119381072","https://openalex.org/W2034033896","https://openalex.org/W2087062149"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"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"}