{"id":"https://openalex.org/W2767639157","doi":"https://doi.org/10.1007/s10589-019-00100-1","title":"Convergence rate for a Radau hp collocation method applied to constrained optimal control","display_name":"Convergence rate for a Radau hp collocation method applied to constrained optimal control","publication_year":2019,"publication_date":"2019-05-02","ids":{"openalex":"https://openalex.org/W2767639157","doi":"https://doi.org/10.1007/s10589-019-00100-1","mag":"2767639157"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-019-00100-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-019-00100-1","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1605.02121","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"William W. Hager","orcid":"https://orcid.org/0000-0003-3132-7017"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"William W. Hager","raw_affiliation_strings":["Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, FL, 32611-8105, USA"],"raw_orcid":"https://orcid.org/0000-0003-3132-7017","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, FL, 32611-8105, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Hongyan Hou","orcid":null},"institutions":[{"id":"https://openalex.org/I166613482","display_name":"Minnesota State University Moorhead","ror":"https://ror.org/03msdae35","country_code":"US","type":"education","lineage":["https://openalex.org/I166613482","https://openalex.org/I91221267"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hongyan Hou","raw_affiliation_strings":["Mathematics Department, Minnesota State University Moorhead, 1104 7th Avenue South, P.O. Box 104, Moorhead, MN, 56563, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Minnesota State University Moorhead, 1104 7th Avenue South, P.O. Box 104, Moorhead, MN, 56563, USA","institution_ids":["https://openalex.org/I166613482"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Subhashree Mohapatra","orcid":null},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Subhashree Mohapatra","raw_affiliation_strings":["Department of Mathematics, University of Florida, Gainesville, FL, 32611, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Florida, Gainesville, FL, 32611, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Anil V. Rao","orcid":null},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anil V. Rao","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of Florida, P.O. Box 116250, Gainesville, FL, 32611-6250, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Florida, P.O. Box 116250, Gainesville, FL, 32611-6250, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":null,"display_name":"Xiang-Sheng Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I79516672","display_name":"University of Louisiana at Lafayette","ror":"https://ror.org/01x8rc503","country_code":"US","type":"education","lineage":["https://openalex.org/I2799628689","https://openalex.org/I79516672"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiang-Sheng Wang","raw_affiliation_strings":["Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, 70503, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, 70503, USA","institution_ids":["https://openalex.org/I79516672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I33213144"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.9119,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.90919274,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"74","issue":"1","first_page":"275","last_page":"314"},"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":0.4758000075817108,"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":0.4758000075817108,"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/T11416","display_name":"Numerical methods for differential equations","score":0.1543000042438507,"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"}},{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.12860000133514404,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/rate-of-convergence","display_name":"Rate of convergence","score":0.5960999727249146},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4975999891757965},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4887999892234802},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.4853000044822693},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4643000066280365},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4163999855518341},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.4043000042438507},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.38019999861717224}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8744000196456909},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5960999727249146},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4975999891757965},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4887999892234802},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.4853000044822693},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47049999237060547},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4643000066280365},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4163999855518341},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.4043000042438507},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.38019999861717224},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.37940001487731934},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.37720000743865967},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.37630000710487366},{"id":"https://openalex.org/C538505008","wikidata":"https://www.wikidata.org/wiki/Q3979448","display_name":"Convergence tests","level":4,"score":0.366100013256073},{"id":"https://openalex.org/C146324458","wikidata":"https://www.wikidata.org/wiki/Q1202673","display_name":"Uniform norm","level":2,"score":0.362199991941452},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.32919999957084656},{"id":"https://openalex.org/C14928880","wikidata":"https://www.wikidata.org/wiki/Q1512559","display_name":"Normal convergence","level":4,"score":0.30790001153945923},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.30660000443458557},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3003000020980835},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.2800999879837036},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27709999680519104},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2709999978542328},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.266400009393692}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10589-019-00100-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-019-00100-1","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1605.02121","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.02121","pdf_url":"https://arxiv.org/pdf/1605.02121","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:RePEc:spr:coopap:v:74:y:2019:i:1:d:10.1007_s10589-019-00100-1","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10589-019-00100-1","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":"pmh:oai:arXiv.org:1605.02121","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.02121","pdf_url":"https://arxiv.org/pdf/1605.02121","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2193832229","display_name":null,"funder_award_id":"N00014-15-1-2048","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G2378547780","display_name":null,"funder_award_id":"N00014-11-1-0068","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G5621868925","display_name":null,"funder_award_id":"N00014-18-1-2100","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W176320170","https://openalex.org/W325655953","https://openalex.org/W1812019903","https://openalex.org/W1972643507","https://openalex.org/W1976377608","https://openalex.org/W1982050100","https://openalex.org/W1988683799","https://openalex.org/W2000226979","https://openalex.org/W2004805052","https://openalex.org/W2005205022","https://openalex.org/W2010533236","https://openalex.org/W2013815604","https://openalex.org/W2017977027","https://openalex.org/W2018816843","https://openalex.org/W2023630575","https://openalex.org/W2027181737","https://openalex.org/W2031291057","https://openalex.org/W2047749334","https://openalex.org/W2049069909","https://openalex.org/W2071166325","https://openalex.org/W2074655580","https://openalex.org/W2080556869","https://openalex.org/W2082642286","https://openalex.org/W2107345353","https://openalex.org/W2109188944","https://openalex.org/W2116146534","https://openalex.org/W2120688585","https://openalex.org/W2130527887","https://openalex.org/W2135320821","https://openalex.org/W2137413756","https://openalex.org/W2145487433","https://openalex.org/W2153425320","https://openalex.org/W2333269921","https://openalex.org/W2500347040","https://openalex.org/W2792013640","https://openalex.org/W2911379030","https://openalex.org/W2941760586","https://openalex.org/W2943889900","https://openalex.org/W4247375400","https://openalex.org/W4253937035","https://openalex.org/W6629776475"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2017-11-17T00:00:00"}