{"id":"https://openalex.org/W2046288051","doi":"https://doi.org/10.1007/s10589-009-9307-9","title":"A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs","display_name":"A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs","publication_year":2009,"publication_date":"2009-12-03","ids":{"openalex":"https://openalex.org/W2046288051","doi":"https://doi.org/10.1007/s10589-009-9307-9","mag":"2046288051"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-009-9307-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-009-9307-9","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"Computational Optimization 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/A5062202097","display_name":"Michael Hinterm\u00fcller","orcid":"https://orcid.org/0000-0001-9471-2479"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]},{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]}],"countries":["AT","DE"],"is_corresponding":true,"raw_author_name":"M. Hinterm\u00fcller","raw_affiliation_strings":["Department of Mathematics and Scientific Computing, Karl-Franzens-University of Graz, Heinrichstrasse 36, 8010, Graz, Austria","Department of Mathematics, Humboldt-University of Berlin, Unter den Linden 6, 10099, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Scientific Computing, Karl-Franzens-University of Graz, Heinrichstrasse 36, 8010, Graz, Austria","institution_ids":["https://openalex.org/I15766117"]},{"raw_affiliation_string":"Department of Mathematics, Humboldt-University of Berlin, Unter den Linden 6, 10099, Berlin, Germany","institution_ids":["https://openalex.org/I39343248"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040677508","display_name":"Ian Kopacka","orcid":"https://orcid.org/0000-0003-4106-1742"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"I. Kopacka","raw_affiliation_strings":["Department of Mathematics and Scientific Computing, Karl-Franzens-University of Graz, Heinrichstrasse 36, 8010, Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Scientific Computing, Karl-Franzens-University of Graz, Heinrichstrasse 36, 8010, Graz, Austria","institution_ids":["https://openalex.org/I15766117"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062202097"],"corresponding_institution_ids":["https://openalex.org/I15766117","https://openalex.org/I39343248"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":2.8125,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.90770926,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"50","issue":"1","first_page":"111","last_page":"145"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9966999888420105,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9954000115394592,"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/mathematics","display_name":"Mathematics","score":0.8526198863983154},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.7467021942138672},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.7456449866294861},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6219719648361206},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5332284569740295},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5326204895973206},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5153038501739502},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5090424418449402},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.47585365176200867},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.4602569043636322},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4333743751049042},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3149471879005432},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.18294638395309448}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8526198863983154},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.7467021942138672},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.7456449866294861},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6219719648361206},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5332284569740295},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5326204895973206},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5153038501739502},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5090424418449402},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.47585365176200867},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.4602569043636322},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4333743751049042},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3149471879005432},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.18294638395309448},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10589-009-9307-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-009-9307-9","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:coopap:v:50:y:2011:i:1:p:111-145","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10589-009-9307-9","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"},{"id":"pmh:oai:unipub.uni-graz.at:134559","is_oa":false,"landing_page_url":"http://unipub.uni-graz.at/doi/doi:10.1007/s10589-009-9307-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306400359","display_name":"Unipub UB Graz (Universit\u00e4t Graz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I15766117","host_organization_name":"University of Graz","host_organization_lineage":["https://openalex.org/I15766117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W217831350","https://openalex.org/W563914728","https://openalex.org/W1492326914","https://openalex.org/W1499054997","https://openalex.org/W1508622707","https://openalex.org/W1516681311","https://openalex.org/W1518792628","https://openalex.org/W1530872699","https://openalex.org/W1559687661","https://openalex.org/W1586623601","https://openalex.org/W1604627832","https://openalex.org/W1965489022","https://openalex.org/W1967755185","https://openalex.org/W1974794583","https://openalex.org/W1976619285","https://openalex.org/W1990088971","https://openalex.org/W1997542937","https://openalex.org/W2004326643","https://openalex.org/W2023884611","https://openalex.org/W2024142617","https://openalex.org/W2026365342","https://openalex.org/W2026938587","https://openalex.org/W2037678919","https://openalex.org/W2042838878","https://openalex.org/W2074190491","https://openalex.org/W2077899785","https://openalex.org/W2113020599","https://openalex.org/W2115178538","https://openalex.org/W2118168201","https://openalex.org/W2120757254","https://openalex.org/W2138849538","https://openalex.org/W2151317657","https://openalex.org/W2258470383","https://openalex.org/W2477073099","https://openalex.org/W2571621221","https://openalex.org/W2605684911","https://openalex.org/W2618681969","https://openalex.org/W3194931891","https://openalex.org/W4230055019","https://openalex.org/W4231147659","https://openalex.org/W4232975436","https://openalex.org/W4249851362","https://openalex.org/W4250690007","https://openalex.org/W4285719527","https://openalex.org/W4292166829","https://openalex.org/W4300592462"],"related_works":["https://openalex.org/W1518141773","https://openalex.org/W2061750202","https://openalex.org/W2128707062","https://openalex.org/W1584005906","https://openalex.org/W2918200358","https://openalex.org/W2043831879","https://openalex.org/W1982186256","https://openalex.org/W1970914972","https://openalex.org/W2051191129","https://openalex.org/W2006148793"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
