{"id":"https://openalex.org/W2015113450","doi":"https://doi.org/10.1137/s1052623400379620","title":"A Squared Smoothing Newton Method for Nonsmooth Matrix Equations and Its Applications in Semidefinite Optimization Problems","display_name":"A Squared Smoothing Newton Method for Nonsmooth Matrix Equations and Its Applications in Semidefinite Optimization Problems","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2015113450","doi":"https://doi.org/10.1137/s1052623400379620","mag":"2015113450"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623400379620","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623400379620","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":true,"oa_status":"green","oa_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/4761/1/Sun_Squared_smoothing_newton.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100618850","display_name":"Jie Sun","orcid":"https://orcid.org/0000-0001-5611-1672"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Jie Sun","raw_affiliation_strings":["National University of Singapore"],"affiliations":[{"raw_affiliation_string":"National University of Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029911976","display_name":"Defeng Sun","orcid":"https://orcid.org/0000-0003-0481-272X"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Defeng Sun","raw_affiliation_strings":["National University of Singapore"],"affiliations":[{"raw_affiliation_string":"National University of Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011886900","display_name":"Liqun Qi","orcid":"https://orcid.org/0000-0002-1112-5250"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Liqun Qi","raw_affiliation_strings":["The Hong Kong Polytechnic University"],"affiliations":[{"raw_affiliation_string":"The Hong Kong Polytechnic University","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100618850"],"corresponding_institution_ids":["https://openalex.org/I165932596"],"apc_list":null,"apc_paid":null,"fwci":6.5455,"has_fulltext":true,"cited_by_count":58,"citation_normalized_percentile":{"value":0.97005445,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"14","issue":"3","first_page":"783","last_page":"806"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":1.0,"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":1.0,"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":0.9990000128746033,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9986000061035156,"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/mathematics","display_name":"Mathematics","score":0.8513548374176025},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.8021635413169861},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.693832278251648},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6295088529586792},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5523725152015686},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.5326029658317566},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.49645668268203735},{"id":"https://openalex.org/keywords/second-order-cone-programming","display_name":"Second-order cone programming","score":0.49045488238334656},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.46771377325057983},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.45855090022087097},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.44901368021965027},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.43449997901916504},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43158605694770813},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4284891188144684},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41957131028175354},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.417934387922287},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.38599875569343567},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.29126662015914917},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.18857821822166443},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.17806601524353027},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11017528176307678},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10584747791290283}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8513548374176025},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.8021635413169861},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.693832278251648},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6295088529586792},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5523725152015686},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.5326029658317566},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.49645668268203735},{"id":"https://openalex.org/C111397411","wikidata":"https://www.wikidata.org/wiki/Q7442977","display_name":"Second-order cone programming","level":4,"score":0.49045488238334656},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.46771377325057983},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.45855090022087097},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.44901368021965027},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.43449997901916504},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43158605694770813},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4284891188144684},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41957131028175354},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.417934387922287},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.38599875569343567},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.29126662015914917},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.18857821822166443},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.17806601524353027},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11017528176307678},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10584747791290283},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s1052623400379620","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623400379620","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"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/4761","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/4761","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/4761/1/Sun_Squared_smoothing_newton.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"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":"Journal/Magazine Article"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/44236","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/44236","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.196.3921","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.196.3921","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.bschool.nus.edu.sg/depart/ds/sunjiehomepage/downloads/publications/ssq.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.307.8255","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.307.8255","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.nus.edu.sg/~matsundf/SSQ_Oct15.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/4761","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/4761","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/4761/1/Sun_Squared_smoothing_newton.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"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":"Journal/Magazine Article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320698","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2015113450.pdf","grobid_xml":"https://content.openalex.org/works/W2015113450.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W333896632","https://openalex.org/W568703599","https://openalex.org/W1543439990","https://openalex.org/W1560867458","https://openalex.org/W1601741115","https://openalex.org/W1632601927","https://openalex.org/W1967969202","https://openalex.org/W1970050176","https://openalex.org/W1980610004","https://openalex.org/W1992688650","https://openalex.org/W2001508169","https://openalex.org/W2003324738","https://openalex.org/W2003583952","https://openalex.org/W2013876250","https://openalex.org/W2021207880","https://openalex.org/W2030566225","https://openalex.org/W2031981531","https://openalex.org/W2038505155","https://openalex.org/W2041638835","https://openalex.org/W2044382581","https://openalex.org/W2046872182","https://openalex.org/W2049763094","https://openalex.org/W2055506505","https://openalex.org/W2068649881","https://openalex.org/W2075379600","https://openalex.org/W2077260542","https://openalex.org/W2086128789","https://openalex.org/W2113734366","https://openalex.org/W2127930751","https://openalex.org/W2142124856","https://openalex.org/W2161496432","https://openalex.org/W2165289170","https://openalex.org/W2224084562","https://openalex.org/W2798707604","https://openalex.org/W3210839039","https://openalex.org/W4230800447","https://openalex.org/W4234065251","https://openalex.org/W4242272985","https://openalex.org/W4245055410","https://openalex.org/W4246146212","https://openalex.org/W4249513058","https://openalex.org/W4255333822"],"related_works":["https://openalex.org/W2352659171","https://openalex.org/W1653317167","https://openalex.org/W2348903644","https://openalex.org/W4375844274","https://openalex.org/W1979163460","https://openalex.org/W2122983719","https://openalex.org/W1978500232","https://openalex.org/W2482087498","https://openalex.org/W2097504558","https://openalex.org/W2015113450"],"abstract_inverted_index":{"Abstract.":[0],"We":[1,51],"study":[2],"a":[3,9,103],"smoothing":[4,106],"Newton":[5],"method":[6,58],"for":[7,29],"solving":[8,30],"nonsmooth":[10],"matrix":[11,107],"equation":[12],"that":[13,68],"includes":[14],"semidefinite":[15,19,31,62],"programming":[16],"and":[17,42,49,96],"the":[18,61,66,69,72,78,82,86,93,100],"complementarity":[20,48,63],"problem":[21,64,73],"as":[22],"special":[23],"cases.":[24],"This":[25],"method,":[26],"if":[27],"specialized":[28],"programs,":[32],"needs":[33],"to":[34,60],"solve":[35],"only":[36],"one":[37],"linear":[38],"system":[39],"per":[40],"iteration":[41],"achieves":[43],"quadratic":[44,54],"convergence":[45,55],"under":[46,65],"strict":[47],"nondegeneracy.":[50],"also":[52],"establish":[53],"of":[56,71,81,99,102,111],"this":[57],"applied":[59],"assumption":[67],"Jacobian":[70],"is":[74],"positive":[75],"definite":[76],"on":[77,92],"affine":[79],"hull":[80],"critical":[83],"cone":[84],"at":[85],"solution.":[87],"These":[88],"results":[89],"are":[90,110],"based":[91],"strong":[94],"semismoothness":[95],"complete":[97],"characterization":[98],"B-subdifferential":[101],"corresponding":[104],"squared":[105],"function,":[108],"which":[109],"general":[112],"theoretical":[113],"interest.":[114]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
