{"id":"https://openalex.org/W1990932715","doi":"https://doi.org/10.1137/130950070","title":"Fast Global Optimization on the Torus, the Sphere, and the Rotation Group","display_name":"Fast Global Optimization on the Torus, the Sphere, and the Rotation Group","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1990932715","doi":"https://doi.org/10.1137/130950070","mag":"1990932715"},"language":"en","primary_location":{"id":"doi:10.1137/130950070","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130950070","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 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/A5009720755","display_name":"Manuel Gr\u00e4f","orcid":"https://orcid.org/0000-0002-9258-9689"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Manuel Gr\u00e4f","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5055215560","display_name":"Ralf Hielscher","orcid":"https://orcid.org/0000-0002-6342-1799"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ralf Hielscher","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":0.3529,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.64290151,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","issue":"1","first_page":"540","last_page":"563"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9970999956130981,"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"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9970999956130981,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9965999722480774,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9937000274658203,"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":0.8078069090843201},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.6201521754264832},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.6010352373123169},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.5308286547660828},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.5238682627677917},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4874603748321533},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.46977800130844116},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4427308440208435},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44265955686569214},{"id":"https://openalex.org/keywords/global-optimization","display_name":"Global optimization","score":0.4204673767089844},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3566720485687256},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3056042194366455},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2281895875930786},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19947335124015808},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13398519158363342}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8078069090843201},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.6201521754264832},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.6010352373123169},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5308286547660828},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.5238682627677917},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4874603748321533},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.46977800130844116},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4427308440208435},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44265955686569214},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.4204673767089844},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3566720485687256},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3056042194366455},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2281895875930786},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19947335124015808},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13398519158363342},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130950070","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130950070","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W89654658","https://openalex.org/W278479801","https://openalex.org/W567568486","https://openalex.org/W1561562988","https://openalex.org/W1579533523","https://openalex.org/W1804110266","https://openalex.org/W1923779967","https://openalex.org/W1967374108","https://openalex.org/W1978833296","https://openalex.org/W1980308545","https://openalex.org/W1986583619","https://openalex.org/W1986655361","https://openalex.org/W1990725792","https://openalex.org/W2003848858","https://openalex.org/W2016939154","https://openalex.org/W2025485823","https://openalex.org/W2025757772","https://openalex.org/W2029671051","https://openalex.org/W2036293114","https://openalex.org/W2040013301","https://openalex.org/W2042071294","https://openalex.org/W2047408599","https://openalex.org/W2058374371","https://openalex.org/W2061171222","https://openalex.org/W2064936877","https://openalex.org/W2066475668","https://openalex.org/W2081237230","https://openalex.org/W2087929700","https://openalex.org/W2091120591","https://openalex.org/W2097607403","https://openalex.org/W2106965455","https://openalex.org/W2110662303","https://openalex.org/W2120062331","https://openalex.org/W2131768055","https://openalex.org/W2133100925","https://openalex.org/W2155750368","https://openalex.org/W2156297272","https://openalex.org/W2495943103","https://openalex.org/W2569750427","https://openalex.org/W3029645440"],"related_works":["https://openalex.org/W2115886818","https://openalex.org/W2466106906","https://openalex.org/W2992877228","https://openalex.org/W2069187387","https://openalex.org/W4250124476","https://openalex.org/W2121922170","https://openalex.org/W3131312709","https://openalex.org/W54027447","https://openalex.org/W2135119351","https://openalex.org/W4210838092"],"abstract_inverted_index":{"Detecting":[0],"all":[1,100],"local":[2],"extrema":[3],"or":[4,16,42],"the":[5,12,14,17,70,73,76,80,105,117,131],"global":[6],"extremum":[7],"of":[8,50,55,72,75,82,94,116,134],"a":[9,21,30,47,95,135],"polynomial":[10,77],"on":[11],"torus,":[13],"sphere,":[15],"rotation":[18],"group":[19],"is":[20,58,120],"tough":[22],"yet":[23],"often":[24],"requested":[25],"numerical":[26],"problem.":[27],"We":[28],"present":[29],"heuristic":[31],"approach":[32,57],"that":[33,63],"applies":[34],"common":[35],"descent":[36,96],"methods":[37,44],"like":[38],"nonlinear":[39],"conjugated":[40],"gradients":[41],"Newtons":[43],"simultaneously":[45,98],"to":[46,69,90,130,141],"large":[48],"number":[49,81],"starting":[51,101,112],"points.":[52,84],"The":[53,114],"cornerstone":[54],"our":[56],"FFT-like":[59,86],"algorithms,":[60],"i.e.,":[61],"algorithms":[62,87,119],"scale":[64],"almost":[65,104],"linearly":[66],"with":[67],"respect":[68],"sum":[71],"dimension":[74],"space":[78],"and":[79],"evaluation":[83],"These":[85],"allow":[88],"us":[89,140],"compute":[91],"one":[92,110],"step":[93],"method":[97],"for":[99,109],"points":[102],"at":[103],"same":[106],"cost":[107],"as":[108],"single":[111],"point.":[113],"effectiveness":[115],"proposed":[118],"demonstrated":[121],"in":[122,144],"various":[123],"applications.":[124],"In":[125],"particular,":[126],"we":[127],"apply":[128],"it":[129],"Radon":[132],"transform":[133],"spherical":[136,145],"function":[137],"which":[138],"allows":[139],"detect":[142],"lines":[143],"patterns.":[146]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}