{"id":"https://openalex.org/W2077260542","doi":"https://doi.org/10.1137/s1052623400380584","title":"Analysis of Nonsmooth Symmetric-Matrix-Valued Functions with Applications to Semidefinite Complementarity Problems","display_name":"Analysis of Nonsmooth Symmetric-Matrix-Valued Functions with Applications to Semidefinite Complementarity Problems","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2077260542","doi":"https://doi.org/10.1137/s1052623400380584","mag":"2077260542"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623400380584","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623400380584","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/A5100363059","display_name":"Xin Chen","orcid":"https://orcid.org/0000-0002-1224-0285"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xin Chen","raw_affiliation_strings":["Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign"],"affiliations":[{"raw_affiliation_string":"Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112621269","display_name":"Houduo Qi","orcid":"https://orcid.org/0000-0003-3481-4814"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Houduo Qi","raw_affiliation_strings":["University Of New south Wales"],"affiliations":[{"raw_affiliation_string":"University Of New south Wales","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110258450","display_name":"Paul Tseng","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul Tseng","raw_affiliation_strings":["University of Washington"],"affiliations":[{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100363059"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":7.8042,"has_fulltext":false,"cited_by_count":95,"citation_normalized_percentile":{"value":0.98106061,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"13","issue":"4","first_page":"960","last_page":"985"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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":0.9995999932289124,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9950000047683716,"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/mathematics","display_name":"Mathematics","score":0.835326075553894},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.749971330165863},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5206314921379089},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.47039708495140076},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43377578258514404},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4298774003982544},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36246174573898315},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.330375611782074}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.835326075553894},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.749971330165863},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5206314921379089},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.47039708495140076},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43377578258514404},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4298774003982544},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36246174573898315},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.330375611782074},{"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s1052623400380584","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623400380584","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:CiteSeerX.psu:10.1.1.57.8708","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.8708","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.washington.edu/~tseng/papers/xxm.ps.Z","raw_type":"text"},{"id":"pmh:oai:eprints.soton.ac.uk:29643","is_oa":false,"landing_page_url":"https://eprints.soton.ac.uk/29643/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W83404773","https://openalex.org/W227419389","https://openalex.org/W391578156","https://openalex.org/W568703599","https://openalex.org/W658559791","https://openalex.org/W1488435683","https://openalex.org/W1502173447","https://openalex.org/W1551360398","https://openalex.org/W1560867458","https://openalex.org/W1575147392","https://openalex.org/W1605807425","https://openalex.org/W1967759264","https://openalex.org/W1980614749","https://openalex.org/W1981229337","https://openalex.org/W1992688650","https://openalex.org/W2001508169","https://openalex.org/W2004596681","https://openalex.org/W2005148680","https://openalex.org/W2023092664","https://openalex.org/W2031981531","https://openalex.org/W2036368324","https://openalex.org/W2040628347","https://openalex.org/W2067547116","https://openalex.org/W2074519406","https://openalex.org/W2113734366","https://openalex.org/W2118811613","https://openalex.org/W2127930751","https://openalex.org/W2142124856","https://openalex.org/W2185657671","https://openalex.org/W2610857016","https://openalex.org/W2798707604","https://openalex.org/W4233526811","https://openalex.org/W4242272985","https://openalex.org/W4245055410","https://openalex.org/W4249513058","https://openalex.org/W4253016148","https://openalex.org/W4255333822"],"related_works":["https://openalex.org/W4286857066","https://openalex.org/W4238239967","https://openalex.org/W1677518548","https://openalex.org/W3213958552","https://openalex.org/W4297812081","https://openalex.org/W2949926331","https://openalex.org/W2754545762","https://openalex.org/W4299562540","https://openalex.org/W4298208753","https://openalex.org/W3175273680"],"abstract_inverted_index":{"For":[0],"any":[1],"function":[2,15,42],"f":[3,29,45],"from":[4,44,68],"$\\mathbb":[5,8],"R$":[6],"to":[7,30,88],"R$,":[9],"one":[10],"can":[11],"define":[12],"a":[13],"corresponding":[14],"on":[16],"the":[17,31,34,46,77,89,98],"space":[18],"of":[19,33,48,80,100],"n":[20,22],"\u00d7":[21],"(block-diagonal)":[23],"real":[24],"symmetric":[25,81],"matrices":[26],"by":[27],"applying":[28],"eigenvalues":[32],"spectral":[35,78],"decomposition.":[36],"We":[37,83],"show":[38],"that":[39],"this":[40,106],"matrix-valued":[41],"inherits":[43],"properties":[47],"continuity,":[49,52],"(local)":[50],"Lipschitz":[51],"directional":[53],"differentiability,":[54,56,58],"Fr\u00e9chet":[55],"continuous":[57],"as":[59,61,71,73],"well":[60,72],"($\\rho$-order)":[62],"semismoothness.":[63],"Our":[64],"analysis":[65,70,99],"uses":[66],"results":[67,87],"nonsmooth":[69],"perturbation":[74],"theory":[75],"for":[76,104],"decomposition":[79],"matrices.":[82],"also":[84],"apply":[85],"our":[86],"semidefinite":[90],"complementarity":[91],"problem,":[92],"addressing":[93],"some":[94],"basic":[95],"issues":[96],"in":[97],"smoothing/semismooth":[101],"Newton":[102],"methods":[103],"solving":[105],"problem.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
