{"id":"https://openalex.org/W2055031148","doi":"https://doi.org/10.1137/050637273","title":"Numerical Sensitivity Analysis for the Quantity of Interest in PDE\u2010Constrained Optimization","display_name":"Numerical Sensitivity Analysis for the Quantity of Interest in PDE\u2010Constrained Optimization","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2055031148","doi":"https://doi.org/10.1137/050637273","mag":"2055031148"},"language":"en","primary_location":{"id":"doi:10.1137/050637273","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050637273","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5109253409","display_name":"Roland Griesse","orcid":null},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"funder","lineage":["https://openalex.org/I138211613"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Roland Griesse","raw_affiliation_strings":["Austrian Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Austrian Academy of Sciences","institution_ids":["https://openalex.org/I138211613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085823095","display_name":"Boris Vexler","orcid":"https://orcid.org/0000-0001-6211-4263"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Boris Vexler","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109253409"],"corresponding_institution_ids":["https://openalex.org/I138211613"],"apc_list":null,"apc_paid":null,"fwci":2.5641,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.88589491,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"29","issue":"1","first_page":"22","last_page":"48"},"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":0.9988999962806702,"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":0.9988999962806702,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9977999925613403,"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/T11416","display_name":"Numerical methods for differential equations","score":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.780055046081543},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6613976955413818},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.6065828800201416},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5921330451965332},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5727958083152771},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.4921943247318268},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4746687412261963},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.47107091546058655},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3518541753292084},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21441146731376648},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09178578853607178}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.780055046081543},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6613976955413818},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.6065828800201416},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5921330451965332},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5727958083152771},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.4921943247318268},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4746687412261963},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.47107091546058655},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3518541753292084},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21441146731376648},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09178578853607178},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/050637273","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050637273","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.722.6201","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.722.6201","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www-m17.ma.tum.de/foswiki/pub/M17/Lehrstuhl/Public/griesse_vexler_2007.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.88.9750","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.88.9750","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ricam.oeaw.ac.at/publications/reports/05/rep05-15.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.90.6160","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.90.6160","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ricam.oeaw.ac.at/people/page/griesse/publications/Second_Order_QOI.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.995.8885","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.995.8885","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.ricam.oeaw.ac.at/files/reports/05/rep05-15.pdf","raw_type":"text"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1658964","is_oa":false,"landing_page_url":"https://mediatum.ub.tum.de/1658964","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1530754727","https://openalex.org/W1965915391","https://openalex.org/W1969272920","https://openalex.org/W1972368368","https://openalex.org/W1977135073","https://openalex.org/W1978174778","https://openalex.org/W2018383942","https://openalex.org/W2026365342","https://openalex.org/W2026463274","https://openalex.org/W2038977026","https://openalex.org/W2045940260","https://openalex.org/W2075205943","https://openalex.org/W2076882792","https://openalex.org/W2091229997","https://openalex.org/W2091525636","https://openalex.org/W2094476291","https://openalex.org/W2136003379","https://openalex.org/W2151325878","https://openalex.org/W2171467378","https://openalex.org/W2182525481","https://openalex.org/W4250028192","https://openalex.org/W4300184951"],"related_works":["https://openalex.org/W2378757965","https://openalex.org/W4224903346","https://openalex.org/W1593262897","https://openalex.org/W2372869593","https://openalex.org/W2384194537","https://openalex.org/W2031011156","https://openalex.org/W1991935520","https://openalex.org/W2368745429","https://openalex.org/W2067940999","https://openalex.org/W2047206873"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"consider":[4],"the":[5,20,36,47,54,67,73,90,108,135,138],"efficient":[6,74],"computation":[7],"of":[8,10,15,22,56,76,92,107,137],"derivatives":[9,63,78],"a":[11,23,85,115,128],"functional":[12],"(the":[13],"quantity":[14,55],"interest)":[16],"which":[17,31,133],"depends":[18],"on":[19],"solution":[21],"PDE\u2010constrained":[24],"optimization":[25,40,110],"problem":[26,41,118,126],"with":[27,53,64,81],"inequality":[28],"constraints":[29],"and":[30,60,122],"may":[32],"be":[33,102],"different":[34],"from":[35],"cost":[37,98],"functional.":[38],"The":[39,96],"is":[42,79,99],"subject":[43],"to":[44,66,101,105],"perturbations":[45],"in":[46,89],"data.":[48],"We":[49],"derive":[50],"conditions":[51],"under":[52],"interest":[57],"possesses":[58],"first":[59],"second":[61],"order":[62],"respect":[65],"perturbation":[68],"parameters.":[69],"An":[70],"algorithm":[71],"for":[72,119,127],"evaluation":[75],"these":[77],"developed,":[80],"considerable":[82],"savings":[83],"over":[84],"direct":[86],"approach,":[87],"especially":[88],"case":[91],"high\u2010dimensional":[93],"parameter":[94,116],"spaces.":[95],"computational":[97],"shown":[100],"small":[103],"compared":[104],"that":[106],"overall":[109],"algorithm.":[111],"Numerical":[112],"experiments":[113],"involving":[114],"identification":[117],"Navier\u2013Stokes":[120],"flow":[121],"an":[123],"optimal":[124],"control":[125],"reaction\u2010diffusion":[129],"system":[130],"are":[131],"presented":[132],"demonstrate":[134],"efficiency":[136],"method.":[139]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}