{"id":"https://openalex.org/W1993692881","doi":"https://doi.org/10.1137/100784369","title":"Heuristic Parameter-Choice Rules for Convex Variational Regularization Based on Error Estimates","display_name":"Heuristic Parameter-Choice Rules for Convex Variational Regularization Based on Error Estimates","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1993692881","doi":"https://doi.org/10.1137/100784369","mag":"1993692881"},"language":"en","primary_location":{"id":"doi:10.1137/100784369","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100784369","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1001.5346","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039605463","display_name":"Bangti Jin","orcid":"https://orcid.org/0000-0002-3775-9155"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bangti Jin","raw_affiliation_strings":["btjin@math.uni-bremen.de#TAB#"],"affiliations":[{"raw_affiliation_string":"btjin@math.uni-bremen.de#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069699303","display_name":"Dirk A. Lorenz","orcid":"https://orcid.org/0000-0002-7419-769X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dirk A. Lorenz","raw_affiliation_strings":["d.lorenz@tu-braunschweig.de#TAB#"],"affiliations":[{"raw_affiliation_string":"d.lorenz@tu-braunschweig.de#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039605463"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7754,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.93104403,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"48","issue":"3","first_page":"1208","last_page":"1229"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994000196456909,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994000196456909,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9994000196456909,"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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":0.7924385070800781},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7923069000244141},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6179166436195374},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.6142303943634033},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6102613806724548},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6039984226226807},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5282791256904602},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5021395683288574},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.456032395362854},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"Variational analysis","score":0.4530503451824188},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.43688642978668213},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12593799829483032},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0776483416557312}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7924385070800781},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7923069000244141},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6179166436195374},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6142303943634033},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6102613806724548},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6039984226226807},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5282791256904602},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5021395683288574},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.456032395362854},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.4530503451824188},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.43688642978668213},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12593799829483032},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0776483416557312},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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":4,"locations":[{"id":"doi:10.1137/100784369","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100784369","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1001.5346","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1001.5346","pdf_url":"https://arxiv.org/pdf/1001.5346","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.756.2802","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.756.2802","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1001.5346.pdf","raw_type":"text"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:1443368","is_oa":false,"landing_page_url":"http://discovery.ucl.ac.uk/1443368/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"   SIAM JOURNAL ON NUMERICAL ANALYSIS , 48  (3)   pp. 1208-1229.   (2010)      ","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1001.5346","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1001.5346","pdf_url":"https://arxiv.org/pdf/1001.5346","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W145616578","https://openalex.org/W1579559187","https://openalex.org/W1594234351","https://openalex.org/W1653619892","https://openalex.org/W1975490585","https://openalex.org/W1986737463","https://openalex.org/W1993118533","https://openalex.org/W1993247264","https://openalex.org/W1995713983","https://openalex.org/W1998762105","https://openalex.org/W2004653286","https://openalex.org/W2005089986","https://openalex.org/W2013830829","https://openalex.org/W2018094386","https://openalex.org/W2023206259","https://openalex.org/W2025495149","https://openalex.org/W2035858287","https://openalex.org/W2037052971","https://openalex.org/W2039918670","https://openalex.org/W2045305026","https://openalex.org/W2063978378","https://openalex.org/W2064880038","https://openalex.org/W2072090418","https://openalex.org/W2081510982","https://openalex.org/W2082823585","https://openalex.org/W2088955745","https://openalex.org/W2094709350","https://openalex.org/W2103559027","https://openalex.org/W2114424556","https://openalex.org/W2115706991","https://openalex.org/W2122825543","https://openalex.org/W2122890444","https://openalex.org/W2126607811","https://openalex.org/W2129131372","https://openalex.org/W2149846618","https://openalex.org/W2296616510","https://openalex.org/W2314826591","https://openalex.org/W2950042078","https://openalex.org/W3098608218","https://openalex.org/W3099047247","https://openalex.org/W3099740457","https://openalex.org/W3101710822","https://openalex.org/W3102241407","https://openalex.org/W3106513112","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W4388311650","https://openalex.org/W5922282","https://openalex.org/W1974056099","https://openalex.org/W4245343541","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W62490179","https://openalex.org/W2954004777","https://openalex.org/W2951102138","https://openalex.org/W2623997598"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"are":[4,16,24,43,62],"interested":[5],"in":[6],"heuristic":[7],"parameter-choice":[8],"rules":[9,23,53,61],"for":[10,45,51,59],"general":[11],"convex":[12],"variational":[13],"regularization":[14],"which":[15],"based":[17],"on":[18],"error":[19,41],"estimates.":[20],"Two":[21],"such":[22],"derived":[25],"and":[26,36,49],"generalize":[27],"those":[28],"from":[29],"quadratic":[30],"regularization,":[31],"namely,":[32],"the":[33,46],"Hanke\u2013Raus":[34,47],"rule":[35],"quasi-optimality":[37],"criterion.":[38],"A":[39],"posteriori":[40],"estimates":[42],"shown":[44],"rule,":[48],"convergence":[50],"both":[52,60],"is":[54],"also":[55],"discussed.":[56],"Numerical":[57],"results":[58],"presented":[63],"to":[64],"illustrate":[65],"their":[66],"applicability.":[67]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}