{"id":"https://openalex.org/W3128670379","doi":"https://doi.org/10.1080/10556788.2020.1850720","title":"Solving SDP Completely with an Interior Point Oracle","display_name":"Solving SDP Completely with an Interior Point Oracle","publication_year":2015,"publication_date":"2015-07-29","ids":{"openalex":"https://openalex.org/W3128670379","doi":"https://doi.org/10.1080/10556788.2020.1850720","mag":"3128670379"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1507.08065","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.08065","pdf_url":"https://arxiv.org/pdf/1507.08065","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"},"type":"preprint","indexed_in":["arxiv"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1507.08065","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005592247","display_name":"Bruno F. Louren\u00e7o","orcid":"https://orcid.org/0000-0003-2369-0107"},"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":true,"raw_author_name":"Louren\\c{c}o, Bruno F.","raw_affiliation_strings":["Department of Statistical Inference and Mathematics, Institute of Statistical Mathematics, Tachikawa, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistical Inference and Mathematics, Institute of Statistical Mathematics, Tachikawa, Japan","institution_ids":["https://openalex.org/I4210134673"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113934718","display_name":"Masakazu Muramatsu","orcid":null},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Muramatsu, Masakazu","raw_affiliation_strings":["Department of Computer and Network Engineering, The University of Electro-Communications, Chofu-shi, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer and Network Engineering, The University of Electro-Communications, Chofu-shi, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"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/I116292333","display_name":"National Graduate Institute for Policy Studies","ror":"https://ror.org/03gz5xp73","country_code":"JP","type":"education","lineage":["https://openalex.org/I116292333"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tsuchiya, Takashi","raw_affiliation_strings":["National Graduate Institute for Policy Studies, Minato-ku, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Graduate Institute for Policy Studies, Minato-ku, Japan","institution_ids":["https://openalex.org/I116292333"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005592247"],"corresponding_institution_ids":["https://openalex.org/I4210134673"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9994000196456909,"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":0.9994000196456909,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9970999956130981,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9930999875068665,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.8530768156051636},{"id":"https://openalex.org/keywords/javascript","display_name":"JavaScript","score":0.8454990983009338},{"id":"https://openalex.org/keywords/zoom","display_name":"Zoom","score":0.6730901002883911},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6649640798568726},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5438083410263062},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.5168696045875549},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4449020028114319},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3628629446029663},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.3360992670059204},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3271747827529907},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32674938440322876},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3137468099594116},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1498824656009674}],"concepts":[{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.8530768156051636},{"id":"https://openalex.org/C544833334","wikidata":"https://www.wikidata.org/wiki/Q2005","display_name":"JavaScript","level":2,"score":0.8454990983009338},{"id":"https://openalex.org/C124913957","wikidata":"https://www.wikidata.org/wiki/Q1232548","display_name":"Zoom","level":3,"score":0.6730901002883911},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6649640798568726},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5438083410263062},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.5168696045875549},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4449020028114319},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3628629446029663},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.3360992670059204},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3271747827529907},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32674938440322876},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3137468099594116},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1498824656009674},{"id":"https://openalex.org/C15336307","wikidata":"https://www.wikidata.org/wiki/Q1766051","display_name":"Lens (geology)","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78762247","wikidata":"https://www.wikidata.org/wiki/Q1273174","display_name":"Petroleum engineering","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:arXiv.org:1507.08065","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.08065","pdf_url":"https://arxiv.org/pdf/1507.08065","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1507.08065","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.08065","pdf_url":"https://arxiv.org/pdf/1507.08065","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[{"display_name":"Industry, innovation and infrastructure","score":0.6399999856948853,"id":"https://metadata.un.org/sdg/9"}],"awards":[{"id":"https://openalex.org/G2363543682","display_name":"Challenge to Intractable Semidefinite and Second-order Cone Programs","funder_award_id":"18H03206","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G262239235","display_name":"Theory and algorithms for ill-conditioned conic linear programming","funder_award_id":"20H04145","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4023687855","display_name":null,"funder_award_id":"(B)20H04145","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4241903736","display_name":null,"funder_award_id":"(B)18H03206","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4475839165","display_name":null,"funder_award_id":"(C)17K00031","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4758419248","display_name":"Solving ill-posed conic optimization problems","funder_award_id":"19K20217","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5617372794","display_name":null,"funder_award_id":"(B)24310112","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7221371476","display_name":null,"funder_award_id":"(B)15H02968","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G732380957","display_name":null,"funder_award_id":"(B)26280005","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7389614848","display_name":null,"funder_award_id":"(C)26330025","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W36849672","https://openalex.org/W1516536271","https://openalex.org/W1519364999","https://openalex.org/W1550331971","https://openalex.org/W1590002045","https://openalex.org/W1632601927","https://openalex.org/W1835789250","https://openalex.org/W1963753244","https://openalex.org/W1964100506","https://openalex.org/W1964916956","https://openalex.org/W1967073510","https://openalex.org/W1987454867","https://openalex.org/W2027889205","https://openalex.org/W2035412546","https://openalex.org/W2035959039","https://openalex.org/W2040321731","https://openalex.org/W2050958701","https://openalex.org/W2054413257","https://openalex.org/W2059854915","https://openalex.org/W2060533249","https://openalex.org/W2062068908","https://openalex.org/W2065056910","https://openalex.org/W2065957732","https://openalex.org/W2080216751","https://openalex.org/W2080359169","https://openalex.org/W2092569137","https://openalex.org/W2104296611","https://openalex.org/W2111625598","https://openalex.org/W2114408464","https://openalex.org/W2134333839","https://openalex.org/W2166161233","https://openalex.org/W2249602763","https://openalex.org/W2275234501","https://openalex.org/W2512467472","https://openalex.org/W2519774166","https://openalex.org/W2549857394","https://openalex.org/W2724786773","https://openalex.org/W2765212321","https://openalex.org/W2778468193","https://openalex.org/W2907897545","https://openalex.org/W2915050298","https://openalex.org/W2962893120","https://openalex.org/W2963029052","https://openalex.org/W2963216318","https://openalex.org/W2963285451","https://openalex.org/W2965171029","https://openalex.org/W2988743386","https://openalex.org/W3008899209","https://openalex.org/W3097101327","https://openalex.org/W3102900599","https://openalex.org/W3103622948","https://openalex.org/W3105686649","https://openalex.org/W3122542532","https://openalex.org/W3124734834","https://openalex.org/W3128670379","https://openalex.org/W4287626374","https://openalex.org/W4288627252","https://openalex.org/W4310294657"],"related_works":["https://openalex.org/W2788595494","https://openalex.org/W2461078469","https://openalex.org/W123790205","https://openalex.org/W2085515337","https://openalex.org/W2244676099","https://openalex.org/W3087706721","https://openalex.org/W4287664162","https://openalex.org/W3172556642","https://openalex.org/W3157456843","https://openalex.org/W1990150827"],"abstract_inverted_index":{"We":[0,24,88],"suppose":[1],"the":[2,81,126,135,143,146,151,162,165],"existence":[3],"of":[4,96,120,128,145,164],"an":[5,28,59,64,69,118],"oracle":[6,29,60],"which":[7,124],"solves":[8],"any":[9],"semidefinite":[10,160],"programming":[11],"(SDP)":[12],"problem":[13,137,148],"satisfying":[14],"Slater's":[15,107],"condition":[16,108],"simultaneously":[17],"at":[18,109],"its":[19],"primal":[20],"and":[21,53,78,138],"dual":[22,144],"sides.":[23,111],"note":[25],"that":[26],"such":[27,58],"might":[30],"not":[31],"be":[32],"able":[33],"to":[34,56,61,105,134,142],"directly":[35],"solve":[36],"general":[37,170],"SDPs":[38],"even":[39],"after":[40],"certain":[41],"regularization":[42],"schemes":[43],"are":[44,103,167],"applied.":[45],"In":[46],"this":[47,51],"work":[48],"we":[49],"fill":[50],"gap":[52],"show":[54],"how":[55],"use":[57],"\"completely":[62],"solve\"":[63],"arbitrary":[65],"SDP.":[66],"Completely":[67],"solving":[68],"SDP,":[70],"includes,":[71],"for":[72,169],"example,":[73],"distinguishing":[74],"between":[75],"weak/strong":[76],"feasibility/infeasibility":[77],"detecting":[79],"when":[80],"optimal":[82],"value":[83],"is":[84,117,125,157],"attained":[85],"or":[86],"not.":[87],"will":[89],"employ":[90],"several":[91],"tools,":[92],"including":[93],"a":[94],"variant":[95],"facial":[97,122,130],"reduction":[98,131],"where":[99],"all":[100,110],"auxiliary":[101],"problems":[102],"ensured":[104],"satisfy":[106],"Our":[112],"main":[113],"technical":[114],"innovation,":[115],"however,":[116],"analysis":[119],"double":[121],"reduction,":[123],"process":[127],"applying":[129],"twice:":[132],"first":[133,152],"original":[136],"then":[139],"once":[140],"more":[141],"regularized":[147],"obtained":[149],"during":[150],"run.":[153],"Although":[154],"our":[155],"discussion":[156],"focused":[158],"on":[159],"programming,":[161],"majority":[163],"results":[166],"proved":[168],"convex":[171],"cones":[172]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2021-02-15T00:00:00"}
