{"id":"https://openalex.org/W2075781693","doi":"https://doi.org/10.1137/s1052623401395899","title":"Further Results on Approximating Nonconvex Quadratic Optimization by Semidefinite Programming Relaxation","display_name":"Further Results on Approximating Nonconvex Quadratic Optimization by Semidefinite Programming Relaxation","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2075781693","doi":"https://doi.org/10.1137/s1052623401395899","mag":"2075781693"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623401395899","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623401395899","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/A5110258450","display_name":"Paul Tseng","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Paul Tseng","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110258450"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1655,"has_fulltext":false,"cited_by_count":81,"citation_normalized_percentile":{"value":0.87338425,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"14","issue":"1","first_page":"268","last_page":"283"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9951000213623047,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9900000095367432,"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.8448209762573242},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8216272592544556},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6618120670318604},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6341009140014648},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.6320892572402954},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5046402215957642},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.46912670135498047},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.43762797117233276},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.3899695873260498},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33611929416656494},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.25183403491973877},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09658896923065186},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09065565466880798},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07351279258728027}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.8448209762573242},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8216272592544556},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6618120670318604},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6341009140014648},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.6320892572402954},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5046402215957642},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.46912670135498047},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.43762797117233276},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.3899695873260498},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33611929416656494},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25183403491973877},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09658896923065186},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09065565466880798},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07351279258728027},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1052623401395899","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623401395899","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W147998453","https://openalex.org/W1518832340","https://openalex.org/W1522995151","https://openalex.org/W1570765209","https://openalex.org/W1582056940","https://openalex.org/W1632601927","https://openalex.org/W1691008300","https://openalex.org/W1723171749","https://openalex.org/W1783633569","https://openalex.org/W1899296442","https://openalex.org/W1963753244","https://openalex.org/W1968745099","https://openalex.org/W1970670479","https://openalex.org/W1985123706","https://openalex.org/W1996754055","https://openalex.org/W2014793162","https://openalex.org/W2035400420","https://openalex.org/W2035532822","https://openalex.org/W2045148236","https://openalex.org/W2074859470","https://openalex.org/W2106264302","https://openalex.org/W2110540077","https://openalex.org/W2495457432","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W2032522442","https://openalex.org/W2055649011","https://openalex.org/W1979163460","https://openalex.org/W2233303476","https://openalex.org/W2024017812","https://openalex.org/W2157555448","https://openalex.org/W3140730696","https://openalex.org/W2149049779","https://openalex.org/W3141756429","https://openalex.org/W1997679962"],"abstract_inverted_index":{"We":[0,170],"study":[1],"approximation":[2],"bounds":[3,100],"for":[4,155,166],"the":[5,24,39,62,72,80,94,156,173],"semidefinite":[6],"programming":[7],"(SDP)":[8],"relaxation":[9],"ofquadratically":[10],"constrained":[11],"quadratic":[12],"optimization:":[13],"$\\min":[14],"f^0(x)$":[15],"subject":[16],"to":[17,55,85],"$f^k(x)\\le":[18],"0$,":[19],"$k=1,\\dots,m$,":[20],"where":[21,76,159],"fk(x)=xTAkx+(bk)Tx+ck.":[22],"In":[23,93],"special":[25,157],"case":[26,158],"of":[27,48,61,135,175],"ellipsoid":[28],"constraints":[29],"with":[30,43,65,178],"interior":[31],"feasible":[32,59],"solution":[33,60],"at":[34,68],"0,":[35],"we":[36,97],"show":[37],"that":[38],"SDP":[40],"relaxation,":[41],"coupled":[42],"a":[44,58],"rank-1":[45],"decomposition":[46],"result":[47],"Sturm":[49],"and":[50,128,131,142,163],"Zhang":[51],"[Math.":[52,122],"Oper.":[53],"Res.,":[54],"appear],":[56],"yields":[57,88],"original":[63],"problem":[64,83],"objective":[66,74],"value":[67],"most":[69],"$(1-\\gamma)^2/(\\sqrt{m}+\\gamma)^2$":[70],"times":[71],"optimal":[73,91],"value,":[75],"$\\gamma=\\sqrt{\\smash[b]{\\max_k":[77],"f^k(0)+1}}$.":[78],"For":[79],"single":[81],"trust-region":[82],"corresponding":[84],"m=1,":[86],"this":[87],"an":[89],"exact":[90],"solution.":[92],"general":[95],"case,":[96],"extend":[98],"some":[99],"derived":[101],"by":[102],"Nesterov":[103],"[Optim.":[104],"Methods":[105],"Softw.,":[106],"9":[107],"(1998),":[108],"pp.":[109,126,153],"141--160;":[110],"working":[111],"paper,":[112],"CORE,":[113],"Universit\u00e9":[114],"Catholique":[115],"de":[116],"Louvain,":[117],"Louvain-la-Neuve,":[118],"Belgium,":[119],"1998],":[120],"Ye":[121,132],"Program.,":[123],"84":[124],"(1999),":[125],"219--226],":[127],"Nesterov,":[129],"Wolkowicz,":[130,139],"[in":[133],"Handbook":[134],"Semidefinite":[136],"Programming,":[137],"H.":[138],"R.":[140],"Saigal,":[141],"L.":[143],"Vandenberghe,":[144],"eds.,":[145],"Kluwer":[146],"Academic":[147],"Publishers,":[148],"Dordrecht,":[149],"The":[150],"Netherlands,":[151],"2000,":[152],"360--419]":[154],"$A^k$":[160],"is":[161],"diagonal":[162],"bk":[164],"=0":[165],"k=1,":[167],"...,":[168],"m.":[169],"also":[171],"discuss":[172],"generation":[174],"approximate":[176],"solutions":[177],"high":[179],"probability.":[180]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
