{"id":"https://openalex.org/W4381432209","doi":"https://doi.org/10.1007/s00180-023-01370-4","title":"Computing T-optimal designs via nested semi-infinite programming and twofold adaptive discretization","display_name":"Computing T-optimal designs via nested semi-infinite programming and twofold adaptive discretization","publication_year":2023,"publication_date":"2023-06-20","ids":{"openalex":"https://openalex.org/W4381432209","doi":"https://doi.org/10.1007/s00180-023-01370-4"},"language":"en","primary_location":{"id":"doi:10.1007/s00180-023-01370-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-023-01370-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-023-01370-4.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"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 Statistics","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/s00180-023-01370-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052132937","display_name":"David Mogalle","orcid":"https://orcid.org/0000-0002-8962-4666"},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"David Mogalle","raw_affiliation_strings":["Fraunhofer Institute for Industrial Mathematics (ITWM), Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany"],"raw_orcid":"https://orcid.org/0000-0002-8962-4666","affiliations":[{"raw_affiliation_string":"Fraunhofer Institute for Industrial Mathematics (ITWM), Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018676887","display_name":"Philipp Seufert","orcid":"https://orcid.org/0000-0002-9343-0434"},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Philipp Seufert","raw_affiliation_strings":["Fraunhofer Institute for Industrial Mathematics (ITWM), Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fraunhofer Institute for Industrial Mathematics (ITWM), Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039125951","display_name":"Jan Schwientek","orcid":"https://orcid.org/0000-0001-9740-3233"},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jan Schwientek","raw_affiliation_strings":["Fraunhofer Institute for Industrial Mathematics (ITWM), Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fraunhofer Institute for Industrial Mathematics (ITWM), Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000192875","display_name":"Michael Bortz","orcid":"https://orcid.org/0000-0001-8169-2907"},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael Bortz","raw_affiliation_strings":["Fraunhofer Institute for Industrial Mathematics (ITWM), Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fraunhofer Institute for Industrial Mathematics (ITWM), Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057344846","display_name":"Karl\u2010Heinz K\u00fcfer","orcid":"https://orcid.org/0000-0001-8612-6445"},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Karl-Heinz K\u00fcfer","raw_affiliation_strings":["Fraunhofer Institute for Industrial Mathematics (ITWM), Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fraunhofer Institute for Industrial Mathematics (ITWM), Fraunhofer-Platz 1, 67663, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5052132937"],"corresponding_institution_ids":["https://openalex.org/I3019415892"],"apc_list":{"value":2490,"currency":"EUR","value_usd":3090},"apc_paid":{"value":2490,"currency":"EUR","value_usd":3090},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11253338,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"39","issue":"5","first_page":"2451","last_page":"2478"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11159","display_name":"Manufacturing Process and Optimization","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"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/T11159","display_name":"Manufacturing Process and Optimization","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T11798","display_name":"Optimal Experimental Design Methods","score":0.9990000128746033,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9975000023841858,"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/sequence","display_name":"Sequence (biology)","score":0.6702768206596375},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6592406034469604},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.587022066116333},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5647178888320923},{"id":"https://openalex.org/keywords/semi-infinite-programming","display_name":"Semi-infinite programming","score":0.5442320704460144},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5201656818389893},{"id":"https://openalex.org/keywords/subroutine","display_name":"Subroutine","score":0.4962838292121887},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.47117120027542114},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.44717714190483093},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4464249610900879},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.43398943543434143},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4163599908351898},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3777141571044922},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36563587188720703},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07880496978759766}],"concepts":[{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6702768206596375},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6592406034469604},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.587022066116333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5647178888320923},{"id":"https://openalex.org/C2780394207","wikidata":"https://www.wikidata.org/wiki/Q7449304","display_name":"Semi-infinite programming","level":3,"score":0.5442320704460144},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5201656818389893},{"id":"https://openalex.org/C96147967","wikidata":"https://www.wikidata.org/wiki/Q190686","display_name":"Subroutine","level":2,"score":0.4962838292121887},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.47117120027542114},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.44717714190483093},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4464249610900879},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.43398943543434143},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4163599908351898},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3777141571044922},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36563587188720703},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07880496978759766},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00180-023-01370-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-023-01370-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-023-01370-4.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"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 Statistics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:compst:v:39:y:2024:i:5:d:10.1007_s00180-023-01370-4","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s00180-023-01370-4","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:publica.fraunhofer.de:publica/445077","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/445077","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"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":"journal article"}],"best_oa_location":{"id":"doi:10.1007/s00180-023-01370-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-023-01370-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-023-01370-4.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"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 Statistics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6899999976158142}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4381432209.pdf"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W180478659","https://openalex.org/W609131506","https://openalex.org/W995630646","https://openalex.org/W1999732211","https://openalex.org/W2008158827","https://openalex.org/W2021674665","https://openalex.org/W2036284542","https://openalex.org/W2043136268","https://openalex.org/W2050045463","https://openalex.org/W2076321036","https://openalex.org/W2093625674","https://openalex.org/W2094444280","https://openalex.org/W2112680240","https://openalex.org/W2115070480","https://openalex.org/W2135205522","https://openalex.org/W2169666393","https://openalex.org/W2242464395","https://openalex.org/W2894520747","https://openalex.org/W2914166403","https://openalex.org/W2962937666","https://openalex.org/W3003257820","https://openalex.org/W3091173904","https://openalex.org/W3103141923","https://openalex.org/W3181422811","https://openalex.org/W3195475456","https://openalex.org/W4229597915","https://openalex.org/W4234118601","https://openalex.org/W4240052069","https://openalex.org/W4242321465","https://openalex.org/W4248074230"],"related_works":["https://openalex.org/W2391861012","https://openalex.org/W2488336788","https://openalex.org/W4285469493","https://openalex.org/W1593224248","https://openalex.org/W2080384954","https://openalex.org/W2375766869","https://openalex.org/W177890044","https://openalex.org/W2053271671","https://openalex.org/W2170474518","https://openalex.org/W1991334712"],"abstract_inverted_index":{"Abstract":[0],"Modelling":[1],"real":[2],"processes":[3],"often":[4],"results":[5],"in":[6,29],"several":[7],"suitable":[8],"models.":[9],"In":[10],"order":[11],"to":[12,15,62],"be":[13,75],"able":[14],"distinguish,":[16],"or":[17,87],"discriminate,":[18],"which":[19,46,73,135],"model":[20,128],"best":[21,60],"represents":[22,68],"a":[23,40,69,78,103,110,154],"phenomenon,":[24],"one":[25,80,100],"is":[26,84,121,183],"interested,":[27],"e.g.,":[28],"so-called":[30],"T-optimal":[31],"designs.":[32],"These":[33],"consist":[34],"of":[35,106,125,141,147,156,163,174],"the":[36,47,55,66,126,142,148,172,188],"(design)":[37],"points":[38],"from":[39,51,177],"generally":[41],"continuous":[42],"design":[43,108,149],"space":[44,150],"at":[45],"models":[48,92],"deviate":[49],"most":[50],"each":[52],"other":[53],"under":[54],"condition":[56],"that":[57,180],"they":[58],"are":[59],"fitted":[61],"those":[63],"points.":[64],"Thus,":[65],"T-criterion":[67],"bi-level":[70],"optimization":[71,116],"problem,":[72,130],"can":[74,186],"transferred":[76],"into":[77],"semi-infinite":[79,115,158],"but":[81],"whose":[82],"solution":[83],"very":[85],"unstable":[86],"time":[88],"consuming":[89],"for":[90],"non-linear":[91],"and":[93,96,137,166,169,185],"non-convex":[94],"lower-":[95],"upper-level":[97],"problems.":[98],"If":[99],"considers":[101],"only":[102,122],"finite":[104],"number":[105],"possible":[107],"points,":[109],"numerically":[111],"well":[112,145],"tractable":[113],"linear":[114,157],"problem":[117],"arises.":[118],"Since":[119],"this":[120],"an":[123,133],"approximation":[124],"original":[127],"discrimination":[129,175],"we":[131],"propose":[132],"algorithm":[134],"alternately":[136],"adaptively":[138],"refines":[139],"discretizations":[140],"parameter":[143],"as":[144,146],"and,":[151],"thus,":[152],"solves":[153],"sequence":[155],"programs.":[159],"We":[160],"prove":[161],"convergence":[162],"our":[164,181],"method":[165],"its":[167],"subroutine":[168],"show":[170],"on":[171],"basis":[173],"tasks":[176],"process":[178],"engineering":[179],"approach":[182],"stable":[184],"outperform":[187],"known":[189],"methods.":[190]},"counts_by_year":[],"updated_date":"2026-02-03T00:53:05.648605","created_date":"2025-10-10T00:00:00"}
