{"id":"https://openalex.org/W4401432054","doi":"https://doi.org/10.1007/s10107-024-02125-9","title":"A radial basis function method for noisy global optimisation","display_name":"A radial basis function method for noisy global optimisation","publication_year":2024,"publication_date":"2024-08-08","ids":{"openalex":"https://openalex.org/W4401432054","doi":"https://doi.org/10.1007/s10107-024-02125-9","pmid":"https://pubmed.ncbi.nlm.nih.gov/40309715"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-024-02125-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-024-02125-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-024-02125-9.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10107-024-02125-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048783857","display_name":"Dirk Banholzer","orcid":null},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Dirk Banholzer","raw_affiliation_strings":["Department of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ UK","Department of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ UK","institution_ids":["https://openalex.org/I43439940"]},{"raw_affiliation_string":"Department of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019337941","display_name":"J\u00f6rg Fliege","orcid":"https://orcid.org/0000-0002-4459-5419"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"J\u00f6rg Fliege","raw_affiliation_strings":["Department of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ UK","Department of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ UK","institution_ids":["https://openalex.org/I43439940"]},{"raw_affiliation_string":"Department of Mathematical Sciences, University of Southampton, Southampton, SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029198420","display_name":"Ralf Werner","orcid":"https://orcid.org/0000-0001-8204-3757"},"institutions":[{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ralf Werner","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, 86159 Augsburg, Germany","Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, 86159, Augsburg, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, 86159 Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, 86159, Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048783857"],"corresponding_institution_ids":["https://openalex.org/I43439940"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12252964,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"211","issue":"1-2","first_page":"49","last_page":"92"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.7056812047958374},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6972426176071167},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.522986650466919},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.502497673034668},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.48257699608802795},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43079033493995667},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42241179943084717},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3514317274093628},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22773340344429016},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21072983741760254},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16861453652381897},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15036332607269287},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.08769649267196655}],"concepts":[{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.7056812047958374},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6972426176071167},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.522986650466919},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.502497673034668},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.48257699608802795},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43079033493995667},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42241179943084717},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3514317274093628},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22773340344429016},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21072983741760254},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16861453652381897},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15036332607269287},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.08769649267196655},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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":5,"locations":[{"id":"doi:10.1007/s10107-024-02125-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-024-02125-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-024-02125-9.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmid:40309715","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40309715","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical programming","raw_type":null},{"id":"pmh:oai:eprints.soton.ac.uk:495039","is_oa":true,"landing_page_url":"http://doi.org/10.1007/s10107-024-02125-9>).","pdf_url":"https://eprints.soton.ac.uk/495039/1/s10107-024-02125-9.pdf","source":{"id":"https://openalex.org/S4306401020","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"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":"PeerReviewed"},{"id":"pmh:oai:pubmedcentral.nih.gov:12037683","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12037683","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC12037683/pdf/10107_2024_Article_2125.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Math Program","raw_type":"Text"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:115083","is_oa":true,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/115083","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.1007/s10107-024-02125-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-024-02125-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-024-02125-9.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3410465595","display_name":"DTA - University of Southampton","funder_award_id":"EP/M50662X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5266142934","display_name":null,"funder_award_id":"EP/M5","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4401432054.pdf","grobid_xml":"https://content.openalex.org/works/W4401432054.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W4617096","https://openalex.org/W624439943","https://openalex.org/W1486164486","https://openalex.org/W1510052597","https://openalex.org/W1573878755","https://openalex.org/W1589534817","https://openalex.org/W1608160849","https://openalex.org/W1967287635","https://openalex.org/W1967569802","https://openalex.org/W1972653858","https://openalex.org/W1988945200","https://openalex.org/W1989011358","https://openalex.org/W1997869834","https://openalex.org/W1999433604","https://openalex.org/W2003724123","https://openalex.org/W2004053964","https://openalex.org/W2020732830","https://openalex.org/W2024697317","https://openalex.org/W2025856991","https://openalex.org/W2059632676","https://openalex.org/W2061144551","https://openalex.org/W2063180182","https://openalex.org/W2063874144","https://openalex.org/W2070330278","https://openalex.org/W2089245375","https://openalex.org/W2093229042","https://openalex.org/W2113741278","https://openalex.org/W2115966511","https://openalex.org/W2123224804","https://openalex.org/W2139983718","https://openalex.org/W2151238122","https://openalex.org/W2170660905","https://openalex.org/W2191881503","https://openalex.org/W2317988884","https://openalex.org/W2338548332","https://openalex.org/W2419199839","https://openalex.org/W2588277129","https://openalex.org/W2889510677","https://openalex.org/W3036152138","https://openalex.org/W3101993717","https://openalex.org/W3144619878","https://openalex.org/W3151594828","https://openalex.org/W3162664130","https://openalex.org/W4251512373","https://openalex.org/W4254772338"],"related_works":["https://openalex.org/W1794182708","https://openalex.org/W2133420660","https://openalex.org/W2387610815","https://openalex.org/W2392320810","https://openalex.org/W2096715552","https://openalex.org/W2078609410","https://openalex.org/W2387724274","https://openalex.org/W431553707","https://openalex.org/W2374946871","https://openalex.org/W1572661297"],"abstract_inverted_index":{"We":[0,114],"present":[1],"a":[2,59,92,105,121,130],"novel":[3],"response":[4],"surface":[5],"method":[6,37,44,90,126],"for":[7,45,81],"global":[8],"optimisation":[9],"of":[10,24,84,104,124,129],"an":[11,47],"expensive":[12,48,86],"and":[13,49,61,75,119],"noisy":[14,27,87],"(black-box)":[15],"objective":[16,51,73],"function,":[17,52],"where":[18],"error":[19],"bounds":[20],"on":[21,40],"the":[22,25,72,85,89,110,125],"deviation":[23],"observed":[26],"function":[28,69,74],"values":[29],"from":[30,58],"their":[31],"true":[32],"counterparts":[33],"are":[34,100],"available.":[35],"The":[36],"is":[38],"based":[39],"Gutmann's":[41],"well-established":[42],"RBF":[43,112],"minimising":[46],"deterministic":[50],"which":[53],"has":[54],"become":[55],"popular":[56],"both":[57],"theoretical":[60],"practical":[62],"perspective.":[63],"To":[64],"construct":[65],"suitable":[66],"radial":[67],"basis":[68],"approximants":[70],"to":[71,76,109],"determine":[77],"new":[78,98],"sample":[79],"points":[80,99],"successive":[82],"evaluation":[83],"objective,":[88],"uses":[91],"regularised":[93],"least-squares":[94],"criterion.":[95],"In":[96],"particular,":[97],"defined":[101],"by":[102,127],"means":[103,128],"target":[106],"value,":[107],"analogous":[108],"original":[111],"method.":[113],"provide":[115,120],"essential":[116],"convergence":[117],"results,":[118],"numerical":[122],"illustration":[123],"simple":[131],"test":[132],"problem.":[133]},"counts_by_year":[],"updated_date":"2026-03-25T14:56:36.534964","created_date":"2025-10-10T00:00:00"}
