{"id":"https://openalex.org/W2792212059","doi":"https://doi.org/10.1137/17m1124036","title":"Minimization Based Formulations of Inverse Problems and Their Regularization","display_name":"Minimization Based Formulations of Inverse Problems and Their Regularization","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2792212059","doi":"https://doi.org/10.1137/17m1124036","mag":"2792212059"},"language":"en","primary_location":{"id":"doi:10.1137/17m1124036","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1124036","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/A5011058927","display_name":"Barbara Kaltenbacher","orcid":"https://orcid.org/0000-0002-3295-6977"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Barbara Kaltenbacher","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011058927"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0295,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.94568088,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"28","issue":"1","first_page":"620","last_page":"645"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T11558","display_name":"Composite Material Mechanics","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.7913651466369629},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7063888311386108},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.639125645160675},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5999873876571655},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5705839395523071},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5173989534378052},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4864944815635681},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16575658321380615},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1484147608280182},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12909027934074402},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08537429571151733}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7913651466369629},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7063888311386108},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.639125645160675},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5999873876571655},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5705839395523071},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5173989534378052},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4864944815635681},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16575658321380615},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1484147608280182},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12909027934074402},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08537429571151733}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1124036","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1124036","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6899999976158142,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G3871119780","display_name":null,"funder_award_id":"P30054","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7909963648","display_name":null,"funder_award_id":"I2271","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320323947","display_name":"K\u00e4rntner Wirtschaftsf\u00f6rderungsfonds","ror":"https://ror.org/050f4mc80"},{"id":"https://openalex.org/F4320325472","display_name":"Alpen-Adria-Universit\u00e4t Klagenfurt","ror":"https://ror.org/05q9m0937"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W335285985","https://openalex.org/W875426949","https://openalex.org/W1570089119","https://openalex.org/W1973166233","https://openalex.org/W1976685335","https://openalex.org/W1985545608","https://openalex.org/W1996589899","https://openalex.org/W1998154728","https://openalex.org/W2002417691","https://openalex.org/W2004105293","https://openalex.org/W2004943774","https://openalex.org/W2019082603","https://openalex.org/W2020408390","https://openalex.org/W2022816471","https://openalex.org/W2027447854","https://openalex.org/W2034511734","https://openalex.org/W2043800538","https://openalex.org/W2045397581","https://openalex.org/W2057265161","https://openalex.org/W2071470146","https://openalex.org/W2094643691","https://openalex.org/W2101232040","https://openalex.org/W2114424556","https://openalex.org/W2132786284","https://openalex.org/W2133560833","https://openalex.org/W2139374946","https://openalex.org/W2327387119","https://openalex.org/W2963117172","https://openalex.org/W2963534696","https://openalex.org/W2963535588","https://openalex.org/W3102747040","https://openalex.org/W3102937250","https://openalex.org/W3105329799","https://openalex.org/W4241668380"],"related_works":["https://openalex.org/W1829060647","https://openalex.org/W1965977581","https://openalex.org/W2061980133","https://openalex.org/W2387685679","https://openalex.org/W4298004047","https://openalex.org/W2077506191","https://openalex.org/W2050855072","https://openalex.org/W3134728064","https://openalex.org/W2374214022","https://openalex.org/W2347781941"],"abstract_inverted_index":{"The":[0],"conventional":[1],"way":[2],"of":[3,10,25,52,90,129,167,187],"formulating":[4,158],"inverse":[5,91,123],"problems":[6],"such":[7,178],"as":[8,42,73,83,116,125,233,235],"identification":[9],"a":[11,53,126,155,214,220,236],"(possibly":[12],"infinite":[13],"dimensional)":[14],"parameter":[15,82,231],"is":[16,22,119],"via":[17,140],"some":[18],"forward":[19,203],"operator,":[20],"which":[21,56],"the":[23,26,30,33,50,65,68,78,81,96,103,112,122,132,148,159,168,174,208,226,240],"concatenation":[24],"observation":[27,69],"operator":[28],"with":[29,77],"parameter-to-state-map":[31],"for":[32,177,207,229,242],"underlying":[34],"model.":[35],"Recently,":[36],"all-at-once":[37,99],"formulations":[38,100,180],"have":[39],"been":[40],"considered":[41,71],"an":[43,130,182],"alternative":[44],"to":[45,60,120,147,195,224],"this":[46,151],"reduced":[47,97],"formulation,":[48],"avoiding":[49],"use":[51],"parameter-to-state":[54],"map,":[55],"would":[57],"sometimes":[58],"lead":[59],"overly":[61],"restrictive":[62],"conditions.":[63],"Here":[64],"model":[66],"and":[67,80,98,105,134,191],"are":[70,199],"simultaneously":[72],"one":[74],"large":[75],"system,":[76],"state":[79,133],"unknowns.":[84],"A":[85],"still":[86],"more":[87],"general":[88],"formulation":[89],"problems,":[92],"containing":[93],"not":[94],"only":[95],"but":[101],"also":[102],"well-known":[104],"highly":[106],"versatile":[107],"variational":[108,179],"approach":[109],"(also":[110],"called":[111],"Kohn--Vogelius":[113,170],"functional":[114],"approach)":[115],"special":[117],"cases,":[118],"formulate":[121],"problem":[124,164,210],"minimization":[127],"problem---instead":[128],"equation---for":[131],"parameter.":[135],"Regularization":[136],"can":[137],"be":[138],"incorporated":[139],"imposing":[141],"constraints":[142,190,218],"and/or":[143],"adding":[144],"regularization":[145,175,188,230],"terms":[146],"objective.":[149],"In":[150,205],"paper,":[152],"after":[153],"giving":[154],"motivation":[156],"by":[157,165,189,192],"electrical":[160],"impedance":[161],"tomography":[162],"(EIT)":[163],"means":[166],"classical":[169],"functional,":[171],"we":[172,211],"explore":[173],"aspects":[176],"in":[181,219],"abstract":[183],"setting.":[184],"Indeed,":[185],"combination":[186],"penalization":[193],"leads":[194],"new":[196],"methods":[197],"that":[198],"applicable":[200],"without":[201],"solving":[202],"problems.":[204],"particular,":[206],"EIT":[209],"will":[212],"consider":[213],"method":[215],"employing":[216],"box":[217],"very":[221],"natural":[222],"manner":[223],"incorporate":[225],"discrepancy":[227],"principle":[228],"choice":[232],"well":[234],"priori":[237],"information":[238],"on":[239],"searched":[241],"conductivity.":[243]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
