{"id":"https://openalex.org/W2051289974","doi":"https://doi.org/10.1137/100795097","title":"Minimizing Condition Number via Convex Programming","display_name":"Minimizing Condition Number via Convex Programming","publication_year":2011,"publication_date":"2011-10-01","ids":{"openalex":"https://openalex.org/W2051289974","doi":"https://doi.org/10.1137/100795097","mag":"2051289974"},"language":"en","primary_location":{"id":"doi:10.1137/100795097","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100795097","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5000609407","display_name":"Zhaosong Lu","orcid":"https://orcid.org/0000-0003-3277-7853"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhaosong Lu","raw_affiliation_strings":["zhaosong@sfu.ca#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"zhaosong@sfu.ca#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065214298","display_name":"Ting Kei Pong","orcid":"https://orcid.org/0000-0001-5862-2986"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ting Kei Pong","raw_affiliation_strings":["tkpong@uw.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"tkpong@uw.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.294,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.86833046,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"32","issue":"4","first_page":"1193","last_page":"1211"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9988999962806702,"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":0.9987999796867371,"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":0.8299095630645752},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8060505390167236},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.6362884044647217},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6265779137611389},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5943549275398254},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5587326288223267},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5143221616744995},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5028912425041199},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.47078651189804077},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4690212309360504},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.4539891481399536},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.44516581296920776},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4405752718448639},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.43225014209747314},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3651133179664612},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.23150989413261414},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.20998671650886536}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.8299095630645752},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8060505390167236},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.6362884044647217},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6265779137611389},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5943549275398254},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5587326288223267},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5143221616744995},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5028912425041199},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.47078651189804077},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4690212309360504},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.4539891481399536},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.44516581296920776},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4405752718448639},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.43225014209747314},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3651133179664612},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.23150989413261414},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.20998671650886536},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100795097","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100795097","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.650.3102","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.650.3102","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.math.sfu.ca/~zhaosong/ResearchPapers/cond_opt_rev.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":17,"referenced_works":["https://openalex.org/W1488435683","https://openalex.org/W1499439642","https://openalex.org/W1553702074","https://openalex.org/W1603765807","https://openalex.org/W1967073510","https://openalex.org/W1973734200","https://openalex.org/W1974329054","https://openalex.org/W1981220107","https://openalex.org/W2026174223","https://openalex.org/W2042860556","https://openalex.org/W2058532290","https://openalex.org/W2066459185","https://openalex.org/W2083042020","https://openalex.org/W2104417092","https://openalex.org/W2143075842","https://openalex.org/W2296319761","https://openalex.org/W3123303526"],"related_works":["https://openalex.org/W3160810049","https://openalex.org/W2036562274","https://openalex.org/W1482750774","https://openalex.org/W2986665254","https://openalex.org/W2121045497","https://openalex.org/W1994349276","https://openalex.org/W2269291726","https://openalex.org/W3204470723","https://openalex.org/W2239063252","https://openalex.org/W2128202699"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"consider":[4],"minimizing":[5],"the":[6,36,40,71,86],"spectral":[7],"condition":[8],"number":[9],"of":[10,39],"a":[11,16,30,46,59,66,104,110,121,134],"positive":[12,51,122,139],"semidefinite":[13,52,60],"matrix":[14],"over":[15],"nonempty":[17],"closed":[18],"convex":[19,31,72,129,135],"set":[20],"$\\Omega$.":[21],"We":[22,63,107,132],"show":[23,78],"that":[24,79,114],"it":[25,54],"can":[26,55],"be":[27,56,147],"solved":[28],"as":[29],"programming":[32,61,73],"problem,":[33,113],"and":[34],"moreover,":[35],"optimal":[37,118,151],"value":[38],"latter":[41],"problem":[42,126],"is":[43,50,82,127],"achievable.":[44],"As":[45],"consequence,":[47],"when":[48,149],"$\\Omega$":[49],"representable,":[53],"cast":[57],"into":[58],"problem.":[62,74],"then":[64],"propose":[65,133],"first-order":[67],"method":[68,81],"to":[69,146],"solve":[70],"The":[75],"computational":[76],"results":[77],"our":[80],"usually":[83],"faster":[84],"than":[85],"standard":[87],"interior":[88],"point":[89],"solver":[90],"SeDuMi":[91],"[J.":[92],"F.":[93],"Sturm,":[94],"Optim.":[95],"Methods":[96],"Softw.,":[97],"11/12":[98],"(1999),":[99],"pp.":[100],"625\u2013653]":[101],"while":[102],"producing":[103],"comparable":[105],"solution.":[106],"also":[108],"study":[109],"closely":[111],"related":[112],"is,":[115],"finding":[116,138,150],"an":[117],"preconditioner":[119],"for":[120,137],"definite":[123,140],"matrix.":[124],"This":[125,142],"not":[128],"in":[130],"general.":[131],"relaxation":[136,143],"preconditioners.":[141,153],"turns":[144],"out":[145],"exact":[148],"diagonal":[152]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}