{"id":"https://openalex.org/W2056061551","doi":"https://doi.org/10.1007/s10957-011-9828-0","title":"A Smoothing Method for Zero\u2013One Constrained Extremum Problems","display_name":"A Smoothing Method for Zero\u2013One Constrained Extremum Problems","publication_year":2011,"publication_date":"2011-04-08","ids":{"openalex":"https://openalex.org/W2056061551","doi":"https://doi.org/10.1007/s10957-011-9828-0","mag":"2056061551"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-011-9828-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-011-9828-0","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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 Optimization Theory and Applications","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/A5102584793","display_name":"Tao Tan","orcid":"https://orcid.org/0009-0001-1083-8769"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Tan","raw_affiliation_strings":["College of Science, Shandong University of Science and Technology, Shandong, 266510, China","Shandong University of Science & Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Shandong University of Science and Technology, Shandong, 266510, China","institution_ids":["https://openalex.org/I80143920"]},{"raw_affiliation_string":"Shandong University of Science & Technology","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100324125","display_name":"Yanyan Li","orcid":"https://orcid.org/0000-0002-2258-8621"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]},{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yanyan Li","raw_affiliation_strings":["College of Science, Shandong University of Science and Technology, Shandong, 266510, China","Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, China","Dalian University of Technology","Shandong University of Science and Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Shandong University of Science and Technology, Shandong, 266510, China","institution_ids":["https://openalex.org/I80143920"]},{"raw_affiliation_string":"Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, China","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"Dalian University of Technology","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"Shandong University of Science and Technology","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013287943","display_name":"Xingsi Li","orcid":null},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xingsi Li","raw_affiliation_strings":["State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China","Dalian Univ of Tech"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China","institution_ids":["https://openalex.org/I27357992"]},{"raw_affiliation_string":"Dalian Univ of Tech","institution_ids":["https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100324125"],"corresponding_institution_ids":["https://openalex.org/I27357992","https://openalex.org/I80143920"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.4516,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63700132,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"150","issue":"1","first_page":"65","last_page":"77"},"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":0.998199999332428,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8357720375061035},{"id":"https://openalex.org/keywords/limit-point","display_name":"Limit point","score":0.7583416700363159},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.637344479560852},{"id":"https://openalex.org/keywords/complementarity-theory","display_name":"Complementarity theory","score":0.6197218894958496},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.544093668460846},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5375838279724121},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5326551795005798},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5230682492256165},{"id":"https://openalex.org/keywords/mixed-complementarity-problem","display_name":"Mixed complementarity problem","score":0.504491925239563},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.4995131492614746},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.49647194147109985},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.49181774258613586},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.4896679222583771},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.4725855588912964},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.44570812582969666},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4375000596046448},{"id":"https://openalex.org/keywords/limit-of-a-sequence","display_name":"Limit of a sequence","score":0.42778488993644714},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39378494024276733},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3769763112068176},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1729370653629303},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17094331979751587}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8357720375061035},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.7583416700363159},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.637344479560852},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.6197218894958496},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.544093668460846},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5375838279724121},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5326551795005798},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5230682492256165},{"id":"https://openalex.org/C77196050","wikidata":"https://www.wikidata.org/wiki/Q6883962","display_name":"Mixed complementarity problem","level":3,"score":0.504491925239563},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.4995131492614746},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.49647194147109985},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.49181774258613586},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4896679222583771},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.4725855588912964},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.44570812582969666},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4375000596046448},{"id":"https://openalex.org/C71287196","wikidata":"https://www.wikidata.org/wiki/Q847204","display_name":"Limit of a sequence","level":3,"score":0.42778488993644714},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39378494024276733},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3769763112068176},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1729370653629303},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17094331979751587},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-011-9828-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-011-9828-0","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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 Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:150:y:2011:i:1:d:10.1007_s10957-011-9828-0","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-011-9828-0","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":[{"score":0.6100000143051147,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W25288802","https://openalex.org/W621833885","https://openalex.org/W1564612581","https://openalex.org/W1720757687","https://openalex.org/W1972577527","https://openalex.org/W1972867892","https://openalex.org/W1987717911","https://openalex.org/W1995240552","https://openalex.org/W2001508169","https://openalex.org/W2006148793","https://openalex.org/W2011044831","https://openalex.org/W2023821846","https://openalex.org/W2025573991","https://openalex.org/W2037678919","https://openalex.org/W2053060496","https://openalex.org/W2055259165","https://openalex.org/W2056723044","https://openalex.org/W2069770680","https://openalex.org/W2075572180","https://openalex.org/W2077136942","https://openalex.org/W2151902790","https://openalex.org/W2155640943","https://openalex.org/W2358151420","https://openalex.org/W3029645440","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W2122617831","https://openalex.org/W2014704055","https://openalex.org/W2050897335","https://openalex.org/W1980455566","https://openalex.org/W2316847856","https://openalex.org/W1966205354","https://openalex.org/W2909617503","https://openalex.org/W4285138912","https://openalex.org/W2006148793","https://openalex.org/W2095246905"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}