{"id":"https://openalex.org/W1977257062","doi":"https://doi.org/10.1137/060650532","title":"Separated Continuous Conic Programming: Strong Duality and an Approximation Algorithm","display_name":"Separated Continuous Conic Programming: Strong Duality and an Approximation Algorithm","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1977257062","doi":"https://doi.org/10.1137/060650532","mag":"1977257062"},"language":"en","primary_location":{"id":"doi:10.1137/060650532","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060650532","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and 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/A5100452949","display_name":"Xiaoqing Wang","orcid":"https://orcid.org/0000-0002-3492-7192"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaoqing Wang","raw_affiliation_strings":["wangxq2@mail.sysu.edu.cn#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"wangxq2@mail.sysu.edu.cn#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089542160","display_name":"Shuzhong Zhang","orcid":"https://orcid.org/0000-0001-5838-1676"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shuzhong Zhang","raw_affiliation_strings":["zhang@se.cuhk.edu.hk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"zhang@se.cuhk.edu.hk#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110433984","display_name":"David D. Yao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David D. Yao","raw_affiliation_strings":["yao@columbia.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"yao@columbia.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8236,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.8894052,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"48","issue":"4","first_page":"2118","last_page":"2138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987999796867371,"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":0.9987999796867371,"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":0.9965000152587891,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/mathematics","display_name":"Mathematics","score":0.8006336688995361},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7149064540863037},{"id":"https://openalex.org/keywords/conic-section","display_name":"Conic section","score":0.6849992871284485},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.648513913154602},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.6421237587928772},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5341737866401672},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5202718377113342},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.4566582143306732},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4434130787849426},{"id":"https://openalex.org/keywords/wolfe-duality","display_name":"Wolfe duality","score":0.4384876787662506},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.3869641125202179},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3661312460899353},{"id":"https://openalex.org/keywords/weak-duality","display_name":"Weak duality","score":0.3438405394554138},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.2997819781303406},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.20727220177650452},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.16465649008750916},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16362613439559937},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07355529069900513}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8006336688995361},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7149064540863037},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.6849992871284485},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.648513913154602},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.6421237587928772},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5341737866401672},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5202718377113342},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.4566582143306732},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4434130787849426},{"id":"https://openalex.org/C109456813","wikidata":"https://www.wikidata.org/wiki/Q8029991","display_name":"Wolfe duality","level":5,"score":0.4384876787662506},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3869641125202179},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3661312460899353},{"id":"https://openalex.org/C80682859","wikidata":"https://www.wikidata.org/wiki/Q7977943","display_name":"Weak duality","level":4,"score":0.3438405394554138},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2997819781303406},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.20727220177650452},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.16465649008750916},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16362613439559937},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07355529069900513},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/060650532","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060650532","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.66.5343","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.66.5343","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ieor.columbia.edu/~yao/sccp3a.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.700.7698","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.700.7698","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.menet.umn.edu/%7Ezhangs/Reports/2009_WZY.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.75.9394","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.75.9394","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.se.cuhk.edu.hk/~zhang/Reports/seem2006-01.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":28,"referenced_works":["https://openalex.org/W564963347","https://openalex.org/W610904500","https://openalex.org/W1518992076","https://openalex.org/W1522531528","https://openalex.org/W1576291835","https://openalex.org/W1967073510","https://openalex.org/W1973403707","https://openalex.org/W1979387334","https://openalex.org/W1985873373","https://openalex.org/W1987611686","https://openalex.org/W1991386000","https://openalex.org/W1994712972","https://openalex.org/W2007960159","https://openalex.org/W2018637736","https://openalex.org/W2021070553","https://openalex.org/W2048512072","https://openalex.org/W2051429641","https://openalex.org/W2054532229","https://openalex.org/W2060451040","https://openalex.org/W2077127687","https://openalex.org/W2084071948","https://openalex.org/W2089105401","https://openalex.org/W2089967443","https://openalex.org/W2094027695","https://openalex.org/W2103843819","https://openalex.org/W2134666018","https://openalex.org/W2161370261","https://openalex.org/W2341171179"],"related_works":["https://openalex.org/W4220928172","https://openalex.org/W3213165575","https://openalex.org/W2029896594","https://openalex.org/W4210245775","https://openalex.org/W2155425983","https://openalex.org/W2085364069","https://openalex.org/W4307261727","https://openalex.org/W1801441248","https://openalex.org/W2152970697","https://openalex.org/W3125150697"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"recent":[2],"applications":[3],"in":[4,8,14],"robust":[5],"optimization":[6,21],"and":[7,54,70],"sign-constrained":[9],"linear-quadratic":[10],"control,":[11],"we":[12,35],"study":[13],"this":[15],"paper":[16],"a":[17,31,37,75,94],"new":[18],"class":[19],"of":[20],"problems":[22],"called":[23],"separated":[24],"continuous":[25],"conic":[26,60],"programming":[27],"(SCCP).":[28],"Focusing":[29],"on":[30],"symmetric":[32],"primal-dual":[33],"pair,":[34],"develop":[36],"strong":[38,83],"duality":[39,84],"theory":[40],"for":[41,86],"the":[42,52,65,82,87,100],"SCCP.":[43,88],"Our":[44],"idea":[45],"is":[46,78],"to":[47,50,57,93,102],"use":[48],"discretization":[49],"connect":[51],"SCCP":[53,101],"its":[55],"dual":[56],"two":[58],"ordinary":[59],"programs.":[61],"We":[62],"show":[63],"if":[64],"latter":[66],"are":[67],"strongly":[68],"feasible":[69],"with":[71],"finite":[72],"optimal":[73],"values,":[74],"condition":[76],"that":[77,98],"readily":[79],"verifiable,":[80],"then":[81],"holds":[85],"This":[89],"approach":[90],"also":[91],"leads":[92],"polynomial-time":[95],"approximation":[96],"algorithm":[97],"solves":[99],"any":[103],"required":[104],"accuracy.":[105]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}