{"id":"https://openalex.org/W4281552282","doi":"https://doi.org/10.1137/20m134664x","title":"An Approximation Scheme for Distributionally Robust PDE-Constrained Optimization","display_name":"An Approximation Scheme for Distributionally Robust PDE-Constrained Optimization","publication_year":2022,"publication_date":"2022-05-26","ids":{"openalex":"https://openalex.org/W4281552282","doi":"https://doi.org/10.1137/20m134664x"},"language":"en","primary_location":{"id":"doi:10.1137/20m134664x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m134664x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and 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/A5028244213","display_name":"Johannes Milz","orcid":"https://orcid.org/0000-0003-3601-3340"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Johannes Milz","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-3601-3340","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014423708","display_name":"Michael Ulbrich","orcid":"https://orcid.org/0000-0002-4320-8616"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Ulbrich","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4495,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.63704073,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"60","issue":"3","first_page":"1410","last_page":"1435"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9891999959945679,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9891999959945679,"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":0.7492782473564148},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6921052932739258},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6542741656303406},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.5952297449111938},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10196128487586975}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7492782473564148},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6921052932739258},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6542741656303406},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.5952297449111938},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10196128487586975}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m134664x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m134664x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3914704962","display_name":"GRK 1754: Optimierung und Numerik f\u00fcr partielle Differentialgleichungen mit nicht glatten Strukturen","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W180711869","https://openalex.org/W1968355947","https://openalex.org/W1973803192","https://openalex.org/W1979836673","https://openalex.org/W2022176369","https://openalex.org/W2038572388","https://openalex.org/W2040960244","https://openalex.org/W2045611427","https://openalex.org/W2048546972","https://openalex.org/W2051421841","https://openalex.org/W2057235791","https://openalex.org/W2066503680","https://openalex.org/W2071614767","https://openalex.org/W2075184363","https://openalex.org/W2080364619","https://openalex.org/W2082686600","https://openalex.org/W2082886722","https://openalex.org/W2087003257","https://openalex.org/W2088411705","https://openalex.org/W2100418324","https://openalex.org/W2101304524","https://openalex.org/W2107979247","https://openalex.org/W2118811613","https://openalex.org/W2125417745","https://openalex.org/W2128095813","https://openalex.org/W2131939929","https://openalex.org/W2137190019","https://openalex.org/W2160578790","https://openalex.org/W2165530668","https://openalex.org/W2166292404","https://openalex.org/W2168170446","https://openalex.org/W2263557086","https://openalex.org/W2461322537","https://openalex.org/W2561737526","https://openalex.org/W2576057118","https://openalex.org/W2592766892","https://openalex.org/W2766727461","https://openalex.org/W2766966154","https://openalex.org/W2780236089","https://openalex.org/W2797722791","https://openalex.org/W2805586941","https://openalex.org/W2806083605","https://openalex.org/W2905334540","https://openalex.org/W2909844392","https://openalex.org/W2946222661","https://openalex.org/W2946543850","https://openalex.org/W2951706529","https://openalex.org/W2963136325","https://openalex.org/W2963538079","https://openalex.org/W2965558357","https://openalex.org/W2967872018","https://openalex.org/W2973491413","https://openalex.org/W2997080082","https://openalex.org/W3004059350","https://openalex.org/W3045847061","https://openalex.org/W3086029161","https://openalex.org/W3120044416","https://openalex.org/W3122712863","https://openalex.org/W3123321780","https://openalex.org/W3144295655","https://openalex.org/W3164869052","https://openalex.org/W3182674788","https://openalex.org/W3204662258"],"related_works":["https://openalex.org/W3005017983","https://openalex.org/W2205708137","https://openalex.org/W3212504317","https://openalex.org/W3182145356","https://openalex.org/W1988872022","https://openalex.org/W2224558845","https://openalex.org/W3028487898","https://openalex.org/W4295680010","https://openalex.org/W2302257968","https://openalex.org/W2051074227"],"abstract_inverted_index":{"We":[0,17,27,69,82],"develop":[1,117],"a":[2,62,66,104,118,123],"sampling-free":[3],"approximation":[4],"scheme":[5],"for":[6,73,89,151],"distributionally":[7,91],"robust":[8,92],"PDE-constrained":[9],"optimization":[10,154],"problems,":[11,100],"which":[12],"are":[13,156],"min-max":[14,58],"control":[15,93],"problems.":[16,81],"define":[18],"the":[19,33,44,48,56,74,84,90,96,109,113,146],"ambiguity":[20],"set":[21],"through":[22],"moment":[23],"and":[24,65,95,98,101],"entropic":[25],"constraints.":[26],"use":[28],"second-order":[29],"Taylor's":[30],"expansions":[31],"of":[32,47,55,86,112,125,128,145],"reduced":[34],"objective":[35,53],"function":[36,50,54],"w.r.t.":[37],"uncertain":[38],"parameters,":[39],"allowing":[40],"us":[41],"to":[42,135,142],"compute":[43,143],"expected":[45],"value":[46,76],"quadratic":[49],"explicitly.":[51],"The":[52,137],"approximated":[57,97,114],"problem":[59,64],"separates":[60],"into":[61],"trust-region":[63],"semidefinite":[67],"program.":[68],"construct":[70],"smoothing":[71,133,147],"functions":[72,77],"optimal":[75,87],"defined":[78],"by":[79],"these":[80],"prove":[83],"existence":[85],"solutions":[88],"problem,":[94,115],"smoothed":[99,129],"show":[102],"that":[103,121],"worst-case":[105],"distribution":[106],"exists.":[107],"For":[108],"numerical":[110],"solution":[111],"we":[116],"homotopy":[119],"method":[120],"computes":[122],"sequence":[124],"stationary":[126],"points":[127],"problems":[130,155],"while":[131],"decreasing":[132],"parameters":[134],"zero.":[136],"adjoint":[138],"approach":[139],"is":[140],"used":[141],"derivatives":[144],"functions.":[148],"Numerical":[149],"results":[150],"two":[152],"nonlinear":[153],"presented.":[157]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-16T07:02:28.622633","created_date":"2025-10-10T00:00:00"}
