{"id":"https://openalex.org/W4405597711","doi":"https://doi.org/10.1007/s00211-024-01448-1","title":"Bilinear control of semilinear elliptic PDEs: convergence of a semismooth Newton method","display_name":"Bilinear control of semilinear elliptic PDEs: convergence of a semismooth Newton method","publication_year":2024,"publication_date":"2024-12-19","ids":{"openalex":"https://openalex.org/W4405597711","doi":"https://doi.org/10.1007/s00211-024-01448-1"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-024-01448-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-024-01448-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-024-01448-1.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-024-01448-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067757319","display_name":"Eduardo Casas","orcid":"https://orcid.org/0000-0002-8364-9416"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Eduardo Casas","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada y Ciencias de la Computaci\u00f3n, E.T.S.I. Industriales y de Telecomunicaci\u00f3n, Universidad de Cantabria, Av. Los Castros s/n, 39005, Santander, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada y Ciencias de la Computaci\u00f3n, E.T.S.I. Industriales y de Telecomunicaci\u00f3n, Universidad de Cantabria, Av. Los Castros s/n, 39005, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024069838","display_name":"Konstantinos Chrysafinos","orcid":null},"institutions":[{"id":"https://openalex.org/I174458059","display_name":"National Technical University of Athens","ror":"https://ror.org/03cx6bg69","country_code":"GR","type":"education","lineage":["https://openalex.org/I174458059"]},{"id":"https://openalex.org/I4210129470","display_name":"FORTH Institute of Applied and Computational Mathematics","ror":"https://ror.org/02n2yp822","country_code":"GR","type":"facility","lineage":["https://openalex.org/I4210129470","https://openalex.org/I8901234"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Konstantinos Chrysafinos","raw_affiliation_strings":["Department of Mathematics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens Zografou Campus, 15780, Athens, Greece","IACM,FORTH, 20013, Heraklion, Crete, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens Zografou Campus, 15780, Athens, Greece","institution_ids":["https://openalex.org/I174458059"]},{"raw_affiliation_string":"IACM,FORTH, 20013, Heraklion, Crete, Greece","institution_ids":["https://openalex.org/I4210129470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054687748","display_name":"Mariano Mateos","orcid":"https://orcid.org/0000-0003-3100-412X"},"institutions":[{"id":"https://openalex.org/I165339363","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02","country_code":"ES","type":"education","lineage":["https://openalex.org/I165339363"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Mariano Mateos","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Campus de Gij\u00f3n, Universidad de Oviedo, 33203, Gij\u00f3n, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Campus de Gij\u00f3n, Universidad de Oviedo, 33203, Gij\u00f3n, Spain","institution_ids":["https://openalex.org/I165339363"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054687748"],"corresponding_institution_ids":["https://openalex.org/I165339363"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":2.0214,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.87384551,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"157","issue":"1","first_page":"143","last_page":"163"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9973999857902527,"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":0.9973999857902527,"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":0.996999979019165,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9966999888420105,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8406394124031067},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7226529717445374},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.6447121500968933},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6288933753967285},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5629479289054871},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.518657386302948},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.48077744245529175},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.4520251750946045},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3801039457321167},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.24375900626182556},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.18833595514297485}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8406394124031067},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7226529717445374},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.6447121500968933},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6288933753967285},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5629479289054871},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.518657386302948},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.48077744245529175},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.4520251750946045},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3801039457321167},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.24375900626182556},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.18833595514297485},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00211-024-01448-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-024-01448-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-024-01448-1.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:repositorio.unican.es:10902/35479","is_oa":true,"landing_page_url":"https://hdl.handle.net/10902/35479","pdf_url":"https://repositorio.unican.es/xmlui/bitstream/10902/35479/3/BilinearControlSmilinear.pdf","source":{"id":"https://openalex.org/S4306400398","display_name":"UCrea (University of Cantabria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13134134","host_organization_name":"Universidad de Cantabria","host_organization_lineage":["https://openalex.org/I13134134"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Numerische Mathematik, 2025, 157(1), 143-163","raw_type":"publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s00211-024-01448-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-024-01448-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-024-01448-1.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1643949827","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2726347730","display_name":null,"funder_award_id":"PID2020-114837GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G300979063","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3114316098","display_name":null,"funder_award_id":"MCIN/ AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5080475149","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7084143925","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7266728691","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7535663061","display_name":null,"funder_award_id":"AEI/10.","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320323823","display_name":"Universidad de Oviedo","ror":"https://ror.org/006gksa02"},{"id":"https://openalex.org/F4320327859","display_name":"Hellenic Foundation for Research and Innovation","ror":null},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405597711.pdf","grobid_xml":"https://content.openalex.org/works/W4405597711.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W581038412","https://openalex.org/W603367508","https://openalex.org/W1551360398","https://openalex.org/W1579781026","https://openalex.org/W1600371943","https://openalex.org/W1993133781","https://openalex.org/W1996088437","https://openalex.org/W2002178240","https://openalex.org/W2026365342","https://openalex.org/W2033071017","https://openalex.org/W2079520492","https://openalex.org/W2091982747","https://openalex.org/W2112867735","https://openalex.org/W2138026757","https://openalex.org/W2159391054","https://openalex.org/W3043796533","https://openalex.org/W3118947097","https://openalex.org/W4293032004","https://openalex.org/W4293775970","https://openalex.org/W4302398722","https://openalex.org/W4404505075"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2165589608","https://openalex.org/W2952139525","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W2340777379","https://openalex.org/W4285277090"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4,57],"carry":[5],"out":[6],"the":[7,10,30,33,42,59,63],"analysis":[8],"of":[9,19,32,41,62],"semismooth":[11,64],"Newton":[12,65],"method":[13,66],"for":[14,29],"control-constrained":[15],"bilinear":[16],"control":[17,43],"problems":[18],"semilinear":[20],"elliptic":[21],"PDEs.":[22],"We":[23],"prove":[24,58],"existence,":[25],"uniqueness":[26],"and":[27,49],"regularity":[28],"solution":[31],"state":[34,45],"equation,":[35],"as":[36,38,77,79],"well":[37,78],"differentiability":[39],"properties":[40],"to":[44,67],"mapping.":[46],"Then,":[47],"first":[48],"second":[50,72],"order":[51,73],"optimality":[52,75],"conditions":[53,76],"are":[54],"obtained.":[55],"Finally,":[56],"superlinear":[60],"convergence":[61],"local":[68],"solutions":[69],"satisfying":[70],"no-gap":[71],"sufficient":[74],"a":[80],"strict":[81],"complementarity":[82],"condition.":[83]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}