{"id":"https://openalex.org/W2172044747","doi":"https://doi.org/10.1137/s1052623402416803","title":"A New Iteration-Complexity Bound for the MTY Predictor-Corrector Algorithm","display_name":"A New Iteration-Complexity Bound for the MTY Predictor-Corrector Algorithm","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2172044747","doi":"https://doi.org/10.1137/s1052623402416803","mag":"2172044747"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623402416803","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623402416803","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/A5108765688","display_name":"Renato D. C. Monteiro","orcid":null},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Renato D. C. Monteiro","raw_affiliation_strings":["#N#\u2021#N#Georgia Institute of Technology#N#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"#N#\u2021#N#Georgia Institute of Technology#N#","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102836195","display_name":"Takashi Tsuchiya","orcid":"https://orcid.org/0000-0003-1878-9401"},"institutions":[{"id":"https://openalex.org/I4210134673","display_name":"The Institute of Statistical Mathematics","ror":"https://ror.org/03jcejr58","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I4210134673","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takashi Tsuchiya","raw_affiliation_strings":["Institute of Statistical Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Statistical Mathematics","institution_ids":["https://openalex.org/I4210134673"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1546,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.88240087,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"15","issue":"2","first_page":"319","last_page":"347"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"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":0.9994999766349792,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9950000047683716,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9890999794006348,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.807479739189148},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6450976133346558},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.6350765228271484},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5416815876960754},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4716305732727051},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45613792538642883},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4244050085544586},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4235846996307373},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3594161868095398},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11491909623146057}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.807479739189148},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6450976133346558},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.6350765228271484},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5416815876960754},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4716305732727051},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45613792538642883},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4244050085544586},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4235846996307373},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3594161868095398},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11491909623146057},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1052623402416803","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623402416803","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:10.1.1.496.5269","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.496.5269","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www2.isye.gatech.edu/~monteiro/publications/tech_reports/layaff.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5600000023841858,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W34169854","https://openalex.org/W47264501","https://openalex.org/W165985421","https://openalex.org/W1509805685","https://openalex.org/W1533868172","https://openalex.org/W1573409602","https://openalex.org/W1966629740","https://openalex.org/W1972223440","https://openalex.org/W1973117121","https://openalex.org/W1978913642","https://openalex.org/W2000957535","https://openalex.org/W2012696830","https://openalex.org/W2014885585","https://openalex.org/W2021505225","https://openalex.org/W2030674458","https://openalex.org/W2032368946","https://openalex.org/W2035532822","https://openalex.org/W2036622774","https://openalex.org/W2049432961","https://openalex.org/W2050897335","https://openalex.org/W2054543516","https://openalex.org/W2059969305","https://openalex.org/W2063176644","https://openalex.org/W2074316151","https://openalex.org/W2076684514","https://openalex.org/W2077875563","https://openalex.org/W2103985627","https://openalex.org/W2127378310","https://openalex.org/W2165452678","https://openalex.org/W2168825111","https://openalex.org/W2467611443","https://openalex.org/W2611147814","https://openalex.org/W4205492143","https://openalex.org/W4241510060","https://openalex.org/W4243297076"],"related_works":["https://openalex.org/W2965106131","https://openalex.org/W2114808974","https://openalex.org/W2094757704","https://openalex.org/W25030584","https://openalex.org/W29231041","https://openalex.org/W2610104823","https://openalex.org/W2074889170","https://openalex.org/W2092044038","https://openalex.org/W2144582354","https://openalex.org/W3125179639"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2,25],"we":[3],"present":[4],"a":[5,41,66,102,159],"new":[6],"iteration-complexity":[7,150,186],"bound":[8,151,187],"for":[9,18,94,152,188],"the":[10,24,29,60,109,116,120,128,135,138,153,168,172,176,184,189],"Mizuno--Todd--Ye":[11],"predictor-corrector":[12],"(MTY":[13],"P-C)":[14],"primal-dual":[15,160],"interior-point":[16],"algorithm":[17,156],"linear":[19,44],"programming.":[20],"The":[21],"analysis":[22,143],"of":[23,32,118,130,137,171,199],"is":[26,101,115],"based":[27],"on":[28,196],"important":[30],"notion":[31],"crossover":[33],"events":[34],"introduced":[35],"by":[36],"Vavasis":[37],"and":[38,99,165,175],"Ye.":[39],"For":[40],"standard":[42],"form":[43],"program":[45],"min{cTx:Ax":[46],"=":[47],"b,":[48],"x":[49],"\\ge":[50],"0}":[51],"with":[52,70,79,108,183],"decision":[53],"variable":[54],"$x\\in":[55],"\\Re^n$,":[56],"e":[57],"show":[58],"that":[59],"MTY":[61,154,190],"P-C":[62,155,191],"algorithm,":[63,192],"started":[64],"from":[65],"well-centered":[67],"interior-feasible":[68,77],"solution":[69,78],"duality":[71,80],"gap":[72,81],"$n":[73],"\\mu_0$,":[74],"finds":[75],"an":[76,145],"less":[82],"than":[83],"$n\\eta$":[84],"in":[85],"${\\cal":[86,146],"O}(T(\\mu_0/\\eta)+n^{3.5}\\log({{\\bar\\chi^*_A}}))$":[87],"iterations,":[88],"where":[89,124,163],"$T(t)\\equiv\\min\\{n^2\\log(\\log":[90],"t)":[91],",\\log":[92],"t\\}$":[93],"all":[95,119],"$t":[96],">":[97],"0$":[98],"${{\\bar\\chi^*_A}}$":[100,114],"scaling":[103],"invariant":[104],"condition":[105],"number":[106],"associated":[107],"matrix":[110,173],"A.":[111],"More":[112],"specifically,":[113],"infimum":[117],"conditions":[121],"numbers":[122],"${\\bar\\chi}_{AD}$,":[123],"D":[125],"varies":[126],"over":[127],"set":[129],"positive":[131],"diagonal":[132],"matrices.":[133],"Under":[134],"setting":[136],"Turing":[139],"machine":[140],"model,":[141],"our":[142],"yields":[144],"O}(n^{3.5}L_A+":[147],"\\min\\{n^2\\log":[148],"L,L\\})$":[149],"to":[157],"find":[158],"optimal":[161],"solution,":[162],"LA":[164],"L":[166,197],"are":[167],"input":[169],"sizes":[170],"A":[174],"data":[177],"(A,b,c),":[178],"respectively.":[179],"This":[180],"contrasts":[181],"well":[182],"classical":[185],"which":[193],"depends":[194],"linearly":[195],"instead":[198],"log":[200],"L.":[201]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}