{"id":"https://openalex.org/W2025132271","doi":"https://doi.org/10.1080/10556780500094697","title":"A pivoting procedure for a class of second-order cone programming","display_name":"A pivoting procedure for a class of second-order cone programming","publication_year":2005,"publication_date":"2005-11-29","ids":{"openalex":"https://openalex.org/W2025132271","doi":"https://doi.org/10.1080/10556780500094697","mag":"2025132271"},"language":"en","primary_location":{"id":"doi:10.1080/10556780500094697","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780500094697","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/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":true,"raw_author_name":"Masakazu Muramatsu","raw_affiliation_strings":["\n The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo, 182-8585, Japan","The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan#TAB#"],"affiliations":[{"raw_affiliation_string":"\n The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo, 182-8585, Japan","institution_ids":["https://openalex.org/I20529979"]},{"raw_affiliation_string":"The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan#TAB#","institution_ids":["https://openalex.org/I20529979"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5113934718"],"corresponding_institution_ids":["https://openalex.org/I20529979"],"apc_list":null,"apc_paid":null,"fwci":0.4241,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.62430323,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"2","first_page":"295","last_page":"315"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9991999864578247,"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":0.9878000020980835,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6752865314483643},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5496039986610413},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.5400228500366211},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5396883487701416},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5337487459182739},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5312568545341492},{"id":"https://openalex.org/keywords/second-order-cone-programming","display_name":"Second-order cone programming","score":0.5021102428436279},{"id":"https://openalex.org/keywords/section","display_name":"Section (typography)","score":0.50174880027771},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4628177881240845},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4584723114967346},{"id":"https://openalex.org/keywords/christian-ministry","display_name":"Christian ministry","score":0.45183974504470825},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4391227066516876},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41113927960395813},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.41016918420791626},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3593171536922455},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2823235094547272},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09040480852127075},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0848519504070282},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.07259267568588257}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6752865314483643},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5496039986610413},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.5400228500366211},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5396883487701416},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5337487459182739},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5312568545341492},{"id":"https://openalex.org/C111397411","wikidata":"https://www.wikidata.org/wiki/Q7442977","display_name":"Second-order cone programming","level":4,"score":0.5021102428436279},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.50174880027771},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4628177881240845},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4584723114967346},{"id":"https://openalex.org/C521751864","wikidata":"https://www.wikidata.org/wiki/Q1729207","display_name":"Christian ministry","level":2,"score":0.45183974504470825},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4391227066516876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41113927960395813},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.41016918420791626},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3593171536922455},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2823235094547272},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09040480852127075},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0848519504070282},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.07259267568588257},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","level":1,"score":0.0},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556780500094697","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780500094697","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309321","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W82689443","https://openalex.org/W1503221585","https://openalex.org/W1543242366","https://openalex.org/W1568307856","https://openalex.org/W1595045940","https://openalex.org/W1980450998","https://openalex.org/W1981027849","https://openalex.org/W2004747456","https://openalex.org/W2006980285","https://openalex.org/W2009923109","https://openalex.org/W2065927298","https://openalex.org/W2074587202","https://openalex.org/W2077274614","https://openalex.org/W2099235735","https://openalex.org/W2105235982","https://openalex.org/W2127470768","https://openalex.org/W2147191663","https://openalex.org/W4301216918"],"related_works":["https://openalex.org/W2949225936","https://openalex.org/W4297030264","https://openalex.org/W2952895455","https://openalex.org/W2536897863","https://openalex.org/W4225000271","https://openalex.org/W2389521946","https://openalex.org/W2518235024","https://openalex.org/W2550463706","https://openalex.org/W2182497102","https://openalex.org/W2053271671"],"abstract_inverted_index":{"Abstract":[0],"We":[1,25,90],"propose":[2,92],"a":[3,7,27,39,48,67,81,101],"pivoting":[4,97],"procedure":[5,98],"for":[6,41,123,138,164],"class":[8,43],"of":[9,44,118,120,133,136,170,182,189],"second-order":[10,17],"cone":[11,107],"programming":[12],"(SOCP)":[13],"problems":[14],"having":[15],"one":[16],"cone,":[18],"but":[19],"possibly":[20],"with":[21],"additional":[22],"non-negative":[23],"variables.":[24],"introduce":[26],"dictionary,":[28],"basic":[29,86],"variables,":[30,32],"nonbasic":[31],"and":[33,187],"other":[34],"necessary":[35],"concepts":[36],"to":[37,55,114,130,159],"define":[38],"pivot":[40,82],"this":[42],"SOCP":[45,51],"problems.":[46],"In":[47],"pivot,":[49],"two-dimensional":[50],"subproblems":[52],"are":[53],"solved":[54],"decide":[56],"which":[57,99,147],"variables":[58],"should":[59],"be":[60],"entering":[61],"or":[62],"leaving":[63],"the":[64,73,84,96,143,149,156,160,168,171,180],"basis.":[65],"Under":[66],"nondegeneracy":[68],"assumption,":[69],"we":[70],"prove":[71],"that":[72],"objective":[74],"function":[75],"value":[76],"is":[77,88,175],"strictly":[78],"decreasing":[79],"by":[80,179],"unless":[83],"current":[85],"solution":[87],"optimal.":[89],"also":[91,128],"an":[93],"algorithm":[94],"using":[95],"has":[100],"global":[102],"convergence":[103],"property.":[104],"Keywords:":[105],"Second-order":[106],"programmingPivoting":[108],"methods":[109],"Acknowledgements":[110],"The":[111,126],"author":[112,127,157],"thanks":[113,129,158],"Professor":[115],"Takashi":[116],"Tsuchiya":[117],"Institute":[119,135],"Statistical":[121],"Mathematics":[122],"stimulating":[124],"discussion.":[125],"Zhaosong":[131],"Lu":[132],"Georgia":[134],"Technology":[137,188],"his":[139],"valuable":[140],"comments":[141,166],"on":[142,167],"case":[144],"\u0169":[145],"0=0,":[146],"lead":[148],"result":[150],"presented":[151],"in":[152,177],"section":[153],"6.":[154],"Finally,":[155],"two":[161],"anonymous":[162],"referees":[163],"their":[165],"presentation":[169],"paper.":[172],"This":[173],"research":[174],"supported":[176],"part":[178],"Ministry":[181],"Education,":[183],"Culture,":[184],"Sports,":[185],"Science":[186],"Japan.":[190]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}