{"id":"https://openalex.org/W4312132305","doi":"https://doi.org/10.1007/s10957-022-02138-4","title":"A Function Approximation Approach for Parametric Optimization","display_name":"A Function Approximation Approach for Parametric Optimization","publication_year":2022,"publication_date":"2022-12-12","ids":{"openalex":"https://openalex.org/W4312132305","doi":"https://doi.org/10.1007/s10957-022-02138-4"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-022-02138-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02138-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02138-4.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","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/s10957-022-02138-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069602662","display_name":"Alberto De Marchi","orcid":"https://orcid.org/0000-0002-3545-6898"},"institutions":[{"id":"https://openalex.org/I40527276","display_name":"Universit\u00e4t der Bundeswehr M\u00fcnchen","ror":"https://ror.org/05kkv3f82","country_code":"DE","type":"education","lineage":["https://openalex.org/I1315109972","https://openalex.org/I40527276","https://openalex.org/I4387152969"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Alberto De Marchi","raw_affiliation_strings":["Institute for Applied Mathematics and Scientific Computing, Department of Aerospace Engineering, Universit\u00e4t der Bundeswehr M\u00fcnchen, Werner-Heisenberg-Weg 39, D-85577, Neubiberg, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Applied Mathematics and Scientific Computing, Department of Aerospace Engineering, Universit\u00e4t der Bundeswehr M\u00fcnchen, Werner-Heisenberg-Weg 39, D-85577, Neubiberg, Germany","institution_ids":["https://openalex.org/I40527276"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046640973","display_name":"Axel Dreves","orcid":"https://orcid.org/0000-0001-9798-0719"},"institutions":[{"id":"https://openalex.org/I40527276","display_name":"Universit\u00e4t der Bundeswehr M\u00fcnchen","ror":"https://ror.org/05kkv3f82","country_code":"DE","type":"education","lineage":["https://openalex.org/I1315109972","https://openalex.org/I40527276","https://openalex.org/I4387152969"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Axel Dreves","raw_affiliation_strings":["Institute for Applied Mathematics and Scientific Computing, Department of Aerospace Engineering, Universit\u00e4t der Bundeswehr M\u00fcnchen, Werner-Heisenberg-Weg 39, D-85577, Neubiberg, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Applied Mathematics and Scientific Computing, Department of Aerospace Engineering, Universit\u00e4t der Bundeswehr M\u00fcnchen, Werner-Heisenberg-Weg 39, D-85577, Neubiberg, Germany","institution_ids":["https://openalex.org/I40527276"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011281312","display_name":"Matthias Gerdts","orcid":"https://orcid.org/0000-0001-8674-5764"},"institutions":[{"id":"https://openalex.org/I40527276","display_name":"Universit\u00e4t der Bundeswehr M\u00fcnchen","ror":"https://ror.org/05kkv3f82","country_code":"DE","type":"education","lineage":["https://openalex.org/I1315109972","https://openalex.org/I40527276","https://openalex.org/I4387152969"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Matthias Gerdts","raw_affiliation_strings":["Institute for Applied Mathematics and Scientific Computing, Department of Aerospace Engineering, Universit\u00e4t der Bundeswehr M\u00fcnchen, Werner-Heisenberg-Weg 39, D-85577, Neubiberg, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Applied Mathematics and Scientific Computing, Department of Aerospace Engineering, Universit\u00e4t der Bundeswehr M\u00fcnchen, Werner-Heisenberg-Weg 39, D-85577, Neubiberg, Germany","institution_ids":["https://openalex.org/I40527276"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020546902","display_name":"Simon Gottschalk","orcid":"https://orcid.org/0000-0003-4305-5290"},"institutions":[{"id":"https://openalex.org/I40527276","display_name":"Universit\u00e4t der Bundeswehr M\u00fcnchen","ror":"https://ror.org/05kkv3f82","country_code":"DE","type":"education","lineage":["https://openalex.org/I1315109972","https://openalex.org/I40527276","https://openalex.org/I4387152969"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Simon Gottschalk","raw_affiliation_strings":["Institute for Applied Mathematics and Scientific Computing, Department of Aerospace Engineering, Universit\u00e4t der Bundeswehr M\u00fcnchen, Werner-Heisenberg-Weg 39, D-85577, Neubiberg, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Applied Mathematics and Scientific Computing, Department of Aerospace Engineering, Universit\u00e4t der Bundeswehr M\u00fcnchen, Werner-Heisenberg-Weg 39, D-85577, Neubiberg, Germany","institution_ids":["https://openalex.org/I40527276"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005756052","display_name":"Sergejs Rogovs","orcid":null},"institutions":[{"id":"https://openalex.org/I40527276","display_name":"Universit\u00e4t der Bundeswehr M\u00fcnchen","ror":"https://ror.org/05kkv3f82","country_code":"DE","type":"education","lineage":["https://openalex.org/I1315109972","https://openalex.org/I40527276","https://openalex.org/I4387152969"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sergejs Rogovs","raw_affiliation_strings":["Institute for Applied Mathematics and Scientific Computing, Department of Aerospace Engineering, Universit\u00e4t der Bundeswehr M\u00fcnchen, Werner-Heisenberg-Weg 39, D-85577, Neubiberg, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Applied Mathematics and Scientific Computing, Department of Aerospace Engineering, Universit\u00e4t der Bundeswehr M\u00fcnchen, Werner-Heisenberg-Weg 39, D-85577, Neubiberg, Germany","institution_ids":["https://openalex.org/I40527276"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5069602662"],"corresponding_institution_ids":["https://openalex.org/I40527276"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.7451,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.76713892,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"196","issue":"1","first_page":"56","last_page":"77"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9997000098228455,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9997000098228455,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994000196456909,"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":0.8198750615119934},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6837839484214783},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.6287598609924316},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5942590236663818},{"id":"https://openalex.org/keywords/test-functions-for-optimization","display_name":"Test functions for optimization","score":0.585551381111145},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5853041410446167},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.548012375831604},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5110481977462769},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47637149691581726},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4480420649051666},{"id":"https://openalex.org/keywords/parametric-programming","display_name":"Parametric programming","score":0.42738598585128784},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.4173262119293213},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.41724205017089844},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.40356433391571045},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26741915941238403},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16183960437774658}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8198750615119934},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6837839484214783},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.6287598609924316},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5942590236663818},{"id":"https://openalex.org/C150185637","wikidata":"https://www.wikidata.org/wiki/Q7705773","display_name":"Test functions for optimization","level":4,"score":0.585551381111145},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5853041410446167},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.548012375831604},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5110481977462769},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47637149691581726},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4480420649051666},{"id":"https://openalex.org/C2776045410","wikidata":"https://www.wikidata.org/wiki/Q25111241","display_name":"Parametric programming","level":3,"score":0.42738598585128784},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4173262119293213},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.41724205017089844},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.40356433391571045},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26741915941238403},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16183960437774658},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10957-022-02138-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02138-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02138-4.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:joptap:v:196:y:2023:i:1:d:10.1007_s10957-022-02138-4","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-022-02138-4","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"}],"best_oa_location":{"id":"doi:10.1007/s10957-022-02138-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10957-022-02138-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10957-022-02138-4.pdf","source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4312132305.pdf","grobid_xml":"https://content.openalex.org/works/W4312132305.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W220525228","https://openalex.org/W386938050","https://openalex.org/W1486164486","https://openalex.org/W1513869646","https://openalex.org/W1551360398","https://openalex.org/W1579057532","https://openalex.org/W1601741115","https://openalex.org/W1607072065","https://openalex.org/W2015374793","https://openalex.org/W2027797374","https://openalex.org/W2059903013","https://openalex.org/W2081698249","https://openalex.org/W2085563112","https://openalex.org/W2095769364","https://openalex.org/W2112862244","https://openalex.org/W2218983664","https://openalex.org/W2326806701","https://openalex.org/W2899283552","https://openalex.org/W2921437394","https://openalex.org/W3046486881","https://openalex.org/W4240873832","https://openalex.org/W4248437491","https://openalex.org/W4251512373","https://openalex.org/W6834789910"],"related_works":["https://openalex.org/W2064551423","https://openalex.org/W2378960857","https://openalex.org/W2083811707","https://openalex.org/W2058692969","https://openalex.org/W3092127437","https://openalex.org/W2007232477","https://openalex.org/W2072692087","https://openalex.org/W2807131660","https://openalex.org/W2066792530","https://openalex.org/W4312778024"],"abstract_inverted_index":{"Abstract":[0],"We":[1,19],"present":[2,100],"a":[3,54,88],"novel":[4],"approach":[5],"for":[6,45],"approximating":[7,41],"the":[8,26,34,74,78,95,106],"primal":[9,35],"and":[10,36,43,72],"dual":[11,37],"parameter-dependent":[12],"solution":[13,52,79],"functions":[14,42,80],"of":[15,25,53,108],"parametric":[16],"optimization":[17],"problems.":[18],"start":[20],"with":[21,39],"an":[22],"equation":[23],"reformulation":[24],"first-order":[27],"necessary":[28],"optimality":[29],"conditions.":[30],"Then,":[31],"we":[32,86,99],"replace":[33],"solutions":[38],"some":[40,46,101],"find":[44],"test":[47,83],"parameters":[48],"optimal":[49],"coefficients":[50],"as":[51],"single":[55],"nonlinear":[56],"least-squares":[57],"problem.":[58],"Under":[59],"mild":[60],"assumptions":[61],"it":[62],"can":[63],"be":[64],"shown":[65],"that":[66,73],"stationary":[67],"points":[68],"are":[69],"global":[70],"minima":[71],"function":[75,90],"approximations":[76],"interpolate":[77],"at":[81],"all":[82],"parameters.":[84],"Further,":[85],"have":[87],"cheap":[89],"evaluation":[91],"criterion":[92],"to":[93],"estimate":[94],"approximation":[96],"error.":[97],"Finally,":[98],"preliminary":[102],"numerical":[103],"results":[104],"showing":[105],"viability":[107],"our":[109],"approach.":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}