{"id":"https://openalex.org/W2024991751","doi":"https://doi.org/10.1137/s1052623496303470","title":"Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions","display_name":"Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2024991751","doi":"https://doi.org/10.1137/s1052623496303470","mag":"2024991751"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623496303470","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623496303470","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/A5005612207","display_name":"Jeffrey C. Lagarias","orcid":"https://orcid.org/0000-0002-4157-5527"},"institutions":[{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jeffrey C. Lagarias","raw_affiliation_strings":["At&T#TAB#"],"affiliations":[{"raw_affiliation_string":"At&T#TAB#","institution_ids":["https://openalex.org/I1283103587"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112197960","display_name":"James A. Reeds","orcid":null},"institutions":[{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James A. Reeds","raw_affiliation_strings":["At&T#TAB#"],"affiliations":[{"raw_affiliation_string":"At&T#TAB#","institution_ids":["https://openalex.org/I1283103587"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103458692","display_name":"Margaret H. Wright","orcid":null},"institutions":[{"id":"https://openalex.org/I1322087612","display_name":"Alcatel Lucent (Germany)","ror":"https://ror.org/00c5mwp75","country_code":"DE","type":"company","lineage":["https://openalex.org/I1322087612"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Margaret H. Wright","raw_affiliation_strings":["Lucent"],"affiliations":[{"raw_affiliation_string":"Lucent","institution_ids":["https://openalex.org/I1322087612"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108373126","display_name":"Paul E. Wright","orcid":null},"institutions":[{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul E. Wright","raw_affiliation_strings":["At&T#TAB#"],"affiliations":[{"raw_affiliation_string":"At&T#TAB#","institution_ids":["https://openalex.org/I1283103587"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5005612207"],"corresponding_institution_ids":["https://openalex.org/I1283103587"],"apc_list":null,"apc_paid":null,"fwci":18.1659,"has_fulltext":false,"cited_by_count":7370,"citation_normalized_percentile":{"value":0.99472063,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"9","issue":"1","first_page":"112","last_page":"147"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9972000122070312,"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":0.9966999888420105,"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":0.8225741982460022},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7146742939949036},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7020329236984253},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.6807354092597961},{"id":"https://openalex.org/keywords/simplex-algorithm","display_name":"Simplex algorithm","score":0.6339120864868164},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.5938291549682617},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5673568248748779},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.46416571736335754},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.42833662033081055},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.30134037137031555},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14666694402694702}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8225741982460022},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7146742939949036},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7020329236984253},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6807354092597961},{"id":"https://openalex.org/C144521790","wikidata":"https://www.wikidata.org/wiki/Q134164","display_name":"Simplex algorithm","level":3,"score":0.6339120864868164},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.5938291549682617},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5673568248748779},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.46416571736335754},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.42833662033081055},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.30134037137031555},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14666694402694702},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1052623496303470","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623496303470","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.120.6062","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.120.6062","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.aoe.vt.edu/~cliff/aoe5244/nelder_mead_2.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1535429593","https://openalex.org/W1965748532","https://openalex.org/W1995832922","https://openalex.org/W2019742812","https://openalex.org/W2054875385","https://openalex.org/W2081989804","https://openalex.org/W2107073443","https://openalex.org/W2170120409","https://openalex.org/W2171074980","https://openalex.org/W2260563454","https://openalex.org/W2499662517","https://openalex.org/W2605471592","https://openalex.org/W2809179212","https://openalex.org/W4244913592"],"related_works":["https://openalex.org/W2133667137","https://openalex.org/W2380756614","https://openalex.org/W4283583523","https://openalex.org/W2384679317","https://openalex.org/W2477407501","https://openalex.org/W1570109187","https://openalex.org/W2366013513","https://openalex.org/W3125083766","https://openalex.org/W4244786412","https://openalex.org/W3143155029"],"abstract_inverted_index":{"Abstract.":[0],"The":[1],"Nelder\u2013Mead":[2,34,43,95,108,134],"simplex":[3,135],"algorithm,":[4],"first":[5],"published":[6],"in":[7,50,83,126],"1965,":[8],"is":[9,102],"an":[10],"enormously":[11],"popular":[12],"direct":[13,131],"search":[14,132],"method":[15,109],"for":[16,32,61,69,92,118],"multidimensional":[17],"unconstrained":[18],"minimization.":[19],"Despite":[20],"its":[21],"widespread":[22],"use,":[23],"essentially":[24],"no":[25],"theoretical":[26],"results":[27,68],"have":[28],"been":[29],"proved":[30,112],"explicitly":[31],"the":[33,42,94,107],"algorithm.":[35],"This":[36],"paper":[37],"presents":[38],"convergence":[39,57,67],"properties":[40],"of":[41,74,79,89,123],"algorithm":[44,96],"applied":[45],"to":[46,58,98,113,115],"strictly":[47,80],"convex":[48,81,124],"functions":[49,82,125],"dimensions":[51,85],"1":[52],"and":[53,64,86],"2.":[54,71],"We":[55],"prove":[56],"a":[59,77,87,99,116,119],"minimizer":[60,117],"dimension":[62,70],"1,":[63],"various":[65],"limited":[66],"A":[72],"counterexample":[73],"McKinnon":[75],"gives":[76],"family":[78],"two":[84,127],"set":[88],"initial":[90],"conditions":[91],"which":[93],"converges":[97],"nonminimizer.":[100],"It":[101],"not":[103],"yet":[104],"known":[105],"whether":[106],"can":[110],"be":[111],"converge":[114],"more":[120],"specialized":[121],"class":[122],"dimensions.":[128],"Key":[129],"words.":[130],"methods,":[133,136],"nonderivative":[137],"optimization":[138],"AMS":[139],"subject":[140],"classifications.":[141],"49D30,":[142],"65K05":[143]},"counts_by_year":[{"year":2026,"cited_by_count":51},{"year":2025,"cited_by_count":316},{"year":2024,"cited_by_count":321},{"year":2023,"cited_by_count":387},{"year":2022,"cited_by_count":373},{"year":2021,"cited_by_count":482},{"year":2020,"cited_by_count":381},{"year":2019,"cited_by_count":395},{"year":2018,"cited_by_count":403},{"year":2017,"cited_by_count":390},{"year":2016,"cited_by_count":370},{"year":2015,"cited_by_count":390},{"year":2014,"cited_by_count":382},{"year":2013,"cited_by_count":418},{"year":2012,"cited_by_count":376}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
