{"id":"https://openalex.org/W1965489022","doi":"https://doi.org/10.1137/080720681","title":"Mathematical Programs with Complementarity Constraints in Function Space: C- and Strong Stationarity and a Path-Following Algorithm","display_name":"Mathematical Programs with Complementarity Constraints in Function Space: C- and Strong Stationarity and a Path-Following Algorithm","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1965489022","doi":"https://doi.org/10.1137/080720681","mag":"1965489022"},"language":"en","primary_location":{"id":"doi:10.1137/080720681","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080720681","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on 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/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"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"M. Hinterm\u00fcller","raw_affiliation_strings":["michael.hintermueller@uni-graz.at#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"michael.hintermueller@uni-graz.at#TAB#","institution_ids":["https://openalex.org/I15766117"]}]},{"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":["ian.kopacka@uni-graz.at#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ian.kopacka@uni-graz.at#TAB#","institution_ids":["https://openalex.org/I15766117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I15766117"],"apc_list":null,"apc_paid":null,"fwci":6.2492,"has_fulltext":false,"cited_by_count":100,"citation_normalized_percentile":{"value":0.96681696,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"20","issue":"2","first_page":"868","last_page":"902"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9988999962806702,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9861999750137329,"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":0.8394577503204346},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.6206251978874207},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5696349740028381},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5611854195594788},{"id":"https://openalex.org/keywords/mixed-complementarity-problem","display_name":"Mixed complementarity problem","score":0.5259155035018921},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.5196322798728943},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5097641348838806},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.4879836440086365},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.45600780844688416},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4556482434272766},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39151865243911743},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1293582320213318},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11337712407112122}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8394577503204346},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.6206251978874207},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5696349740028381},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5611854195594788},{"id":"https://openalex.org/C77196050","wikidata":"https://www.wikidata.org/wiki/Q6883962","display_name":"Mixed complementarity problem","level":3,"score":0.5259155035018921},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.5196322798728943},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5097641348838806},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.4879836440086365},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.45600780844688416},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4556482434272766},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39151865243911743},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1293582320213318},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11337712407112122},{"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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/080720681","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080720681","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:unipub.uni-graz.at:133190","is_oa":false,"landing_page_url":"http://resolver.obvsg.at/urn:nbn:at:at-ubg:3-1163","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":0.49000000953674316,"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":39,"referenced_works":["https://openalex.org/W175246081","https://openalex.org/W193038848","https://openalex.org/W753785187","https://openalex.org/W1495442750","https://openalex.org/W1505930614","https://openalex.org/W1508622707","https://openalex.org/W1516681311","https://openalex.org/W1518792628","https://openalex.org/W1543439990","https://openalex.org/W1604627832","https://openalex.org/W1967755185","https://openalex.org/W1976619285","https://openalex.org/W1977135073","https://openalex.org/W1990088971","https://openalex.org/W1992688650","https://openalex.org/W1997472590","https://openalex.org/W2002230262","https://openalex.org/W2007753746","https://openalex.org/W2016570470","https://openalex.org/W2026365342","https://openalex.org/W2034370145","https://openalex.org/W2037678919","https://openalex.org/W2038125339","https://openalex.org/W2038896843","https://openalex.org/W2042838878","https://openalex.org/W2046074066","https://openalex.org/W2048777767","https://openalex.org/W2067547116","https://openalex.org/W2070289182","https://openalex.org/W2074190491","https://openalex.org/W2087003257","https://openalex.org/W2120757254","https://openalex.org/W2127556239","https://openalex.org/W2138849538","https://openalex.org/W2153562582","https://openalex.org/W2490697967","https://openalex.org/W2605684911","https://openalex.org/W2985272081","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3118444755","https://openalex.org/W2128234186","https://openalex.org/W2276648117","https://openalex.org/W2391525457","https://openalex.org/W819098253","https://openalex.org/W2085014864","https://openalex.org/W2144455869","https://openalex.org/W190854043","https://openalex.org/W2350200292","https://openalex.org/W2374008704"],"abstract_inverted_index":{"An":[0],"optimal":[1],"control":[2],"problem":[3,17],"governed":[4],"by":[5,76,92],"an":[6],"elliptic":[7],"variational":[8],"inequality":[9],"is":[10,18,24,57,85,90],"studied.":[11,71],"The":[12,72,81],"feasible":[13],"set":[14],"of":[15,46,94],"the":[16,28,31,39,52],"relaxed,":[19],"and":[20,44,54,62,87,101],"a":[21,102],"path\u2013following-type":[22],"method":[23],"used":[25],"to":[26,51],"regularize":[27],"constraint":[29],"on":[30],"state":[32],"variable.":[33],"First":[34],"order":[35],"optimality":[36],"conditions":[37],"for":[38],"relaxed-regularized":[40],"subproblems":[41,73],"are":[42,70,74],"derived,":[43],"convergence":[45],"stationary":[47],"points":[48],"with":[49,98],"respect":[50],"relaxation":[53],"regularization":[55],"parameters":[56],"shown.":[58],"In":[59],"particular,":[60],"C-":[61],"strong":[63],"stationarity":[64],"as":[65,67],"well":[66],"variants":[68],"thereof":[69],"solved":[75],"using":[77],"semismooth":[78],"Newton":[79],"methods.":[80],"overall":[82],"algorithmic":[83],"concept":[84],"provided,":[86],"its":[88],"performance":[89],"discussed":[91],"means":[93],"examples,":[95],"including":[96],"problems":[97],"bilateral":[99],"constraints":[100],"nonsymmetric":[103],"operator.":[104]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}