{"id":"https://openalex.org/W3208779373","doi":"https://doi.org/10.1007/s10589-022-00370-2","title":"A path-following inexact Newton method for PDE-constrained optimal control in BV","display_name":"A path-following inexact Newton method for PDE-constrained optimal control in BV","publication_year":2022,"publication_date":"2022-05-11","ids":{"openalex":"https://openalex.org/W3208779373","doi":"https://doi.org/10.1007/s10589-022-00370-2","mag":"3208779373"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-022-00370-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-022-00370-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-022-00370-2.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10589-022-00370-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027643639","display_name":"Dominik Hafemeyer","orcid":"https://orcid.org/0000-0002-9161-4811"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"D. Hafemeyer","raw_affiliation_strings":["Lehrstuhl f\u00fcr Optimalsteuerung, Department of Mathematics, TU M\u00fcnchen, Boltzmannstr. 3, 85748, Garching b. M\u00fcnchen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehrstuhl f\u00fcr Optimalsteuerung, Department of Mathematics, TU M\u00fcnchen, Boltzmannstr. 3, 85748, Garching b. M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049624284","display_name":"Florian Mannel","orcid":"https://orcid.org/0000-0001-9042-0428"},"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":true,"raw_author_name":"F. Mannel","raw_affiliation_strings":["Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstra\u00dfe 36, 8010, Graz, Austria"],"raw_orcid":"https://orcid.org/0000-0001-9042-0428","affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstra\u00dfe 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/A5049624284"],"corresponding_institution_ids":["https://openalex.org/I15766117"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.6645,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.59345327,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"82","issue":"3","first_page":"753","last_page":"794"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9975000023841858,"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":0.9973000288009644,"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":0.6931882500648499},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.657450795173645},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6012588739395142},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5734148025512695},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5706421136856079},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5596238374710083},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5516610145568848},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5377210974693298},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5304707288742065},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5120161175727844},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.477690726518631},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.46542781591415405},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4459708333015442},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4187888503074646},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.362835168838501},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2974205017089844},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15868091583251953},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08779597282409668}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6931882500648499},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.657450795173645},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6012588739395142},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5734148025512695},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5706421136856079},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5596238374710083},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5516610145568848},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5377210974693298},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5304707288742065},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5120161175727844},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.477690726518631},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.46542781591415405},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4459708333015442},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4187888503074646},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.362835168838501},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2974205017089844},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15868091583251953},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08779597282409668},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10589-022-00370-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-022-00370-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-022-00370-2.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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:82:y:2022:i:3:d:10.1007_s10589-022-00370-2","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10589-022-00370-2","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:mediatum.ub.tum.de:node/1659515","is_oa":false,"landing_page_url":"https://mediatum.ub.tum.de/1659515","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1792958","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1792958","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10589-022-00370-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-022-00370-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-022-00370-2.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1277698726","display_name":null,"funder_award_id":"188264188/GRK1754","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3914704962","display_name":null,"funder_award_id":"188264188","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320322572","display_name":"Studienstiftung des Deutschen Volkes","ror":"https://ror.org/05xwwfy96"},{"id":"https://openalex.org/F4320323383","display_name":"Technische Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/02kkvpp62"},{"id":"https://openalex.org/F4320325582","display_name":"Karl-Franzens-Universit\u00e4t Graz","ror":"https://ror.org/01faaaf77"},{"id":"https://openalex.org/F4320335337","display_name":"Elitenetzwerk Bayern","ror":null},{"id":"https://openalex.org/F4320335380","display_name":"Graduate School, Technische Universit\u00e4t M\u00fcnchen","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3208779373.pdf","grobid_xml":"https://content.openalex.org/works/W3208779373.grobid-xml"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W22526763","https://openalex.org/W73123583","https://openalex.org/W106485379","https://openalex.org/W1480714962","https://openalex.org/W1523263384","https://openalex.org/W1575147392","https://openalex.org/W1586623601","https://openalex.org/W1594563152","https://openalex.org/W1601728065","https://openalex.org/W1969518673","https://openalex.org/W1972419797","https://openalex.org/W1973494638","https://openalex.org/W1979159785","https://openalex.org/W1981159109","https://openalex.org/W1981343212","https://openalex.org/W1983938029","https://openalex.org/W1985093954","https://openalex.org/W1986850130","https://openalex.org/W2007176686","https://openalex.org/W2017848200","https://openalex.org/W2030036911","https://openalex.org/W2034511734","https://openalex.org/W2035226238","https://openalex.org/W2037124131","https://openalex.org/W2057410521","https://openalex.org/W2067736594","https://openalex.org/W2093742335","https://openalex.org/W2095140771","https://openalex.org/W2103559027","https://openalex.org/W2108454125","https://openalex.org/W2114476378","https://openalex.org/W2121613024","https://openalex.org/W2121617946","https://openalex.org/W2128095813","https://openalex.org/W2135557790","https://openalex.org/W2143476164","https://openalex.org/W2147335602","https://openalex.org/W2212370034","https://openalex.org/W2300900742","https://openalex.org/W2314511028","https://openalex.org/W2411049225","https://openalex.org/W2527369378","https://openalex.org/W2527526908","https://openalex.org/W2595348797","https://openalex.org/W2621637713","https://openalex.org/W2748342193","https://openalex.org/W2748532759","https://openalex.org/W2962700545","https://openalex.org/W2963638310","https://openalex.org/W2963871489","https://openalex.org/W2968091021","https://openalex.org/W2995178964","https://openalex.org/W3043016105","https://openalex.org/W3046012800","https://openalex.org/W3100335443","https://openalex.org/W3208779373","https://openalex.org/W4206097460","https://openalex.org/W4236384742","https://openalex.org/W4245654886","https://openalex.org/W4246234513","https://openalex.org/W4250589301","https://openalex.org/W4300657400"],"related_works":["https://openalex.org/W2383807498","https://openalex.org/W1978572805","https://openalex.org/W1997992934","https://openalex.org/W1987225439","https://openalex.org/W4238188170","https://openalex.org/W2125114371","https://openalex.org/W4213275102","https://openalex.org/W2151138761","https://openalex.org/W2620315894","https://openalex.org/W2050481923"],"abstract_inverted_index":{"Abstract":[0],"We":[1,27,51,106,136],"study":[2],"a":[3,29,87,110,115,138],"PDE-constrained":[4],"optimal":[5],"control":[6,23,97],"problem":[7,72,141],"that":[8,37,75],"involves":[9],"functions":[10],"of":[11,21,61,69,89,102,109,156],"bounded":[12],"variation":[13],"as":[14,99,121],"controls":[15],"and":[16,44,128,146,154],"includes":[17],"the":[18,22,25,35,41,59,67,70,90,96,103,124,152,157],"TV":[19,42],"seminorm":[20,43],"in":[24,53,94],"objective.":[26],"apply":[28],"path-following":[30,134],"inexact":[31,77,118,133],"Newton":[32,78,119],"method":[33,79,120],"to":[34,66,86,150],"problems":[36,64],"arise":[38],"from":[39],"smoothing":[40],"adding":[45],"an":[46,54,76,132],"$$H^1$$":[47],"<mml:math":[48],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math>":[49],"regularization.":[50],"prove":[52],"infinite-dimensional":[55],"setting":[56],"that,":[57],"first,":[58],"solutions":[60],"these":[62],"auxiliary":[63,91,126],"converge":[65],"solution":[68,145],"original":[71],"and,":[73],"second,":[74],"enjoys":[80],"fast":[81],"local":[82],"convergence":[83,108],"when":[84],"applied":[85],"reformulation":[88],"optimality":[92],"systems":[93],"which":[95],"appears":[98],"implicit":[100],"function":[101],"adjoint":[104],"state.":[105],"show":[107],"Finite":[111],"Element":[112],"approximation,":[113],"provide":[114],"globalized":[116],"preconditioned":[117],"solver":[122],"for":[123],"discretized":[125],"problems,":[127],"embed":[129],"it":[130],"into":[131],"scheme.":[135],"construct":[137],"two-dimensional":[139],"test":[140],"with":[142],"fully":[143],"explicit":[144],"present":[147],"numerical":[148],"results":[149],"illustrate":[151],"accuracy":[153],"robustness":[155],"approach.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
