{"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":true,"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, Santander, Spain","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, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]},{"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":true,"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, Athens, Greece","IACM,FORTH, Heraklion, Crete, Greece","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, Athens, Greece","institution_ids":["https://openalex.org/I174458059"]},{"raw_affiliation_string":"IACM,FORTH, Heraklion, Crete, Greece","institution_ids":["https://openalex.org/I4210129470"]},{"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, Gij\u00f3n, Spain","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, Gij\u00f3n, Spain","institution_ids":["https://openalex.org/I165339363"]},{"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":4,"corresponding_author_ids":["https://openalex.org/A5024069838","https://openalex.org/A5054687748","https://openalex.org/A5067757319"],"corresponding_institution_ids":["https://openalex.org/I13134134","https://openalex.org/I165339363","https://openalex.org/I174458059","https://openalex.org/I4210129470"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":1.6427,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.84131227,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"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":"info:eu-repo/semantics/article"}],"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":{"grobid_xml":true,"pdf":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":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
