{"id":"https://openalex.org/W2025702035","doi":"https://doi.org/10.1137/06065622x","title":"Majorizing Functions and Convergence of the Gauss\u2013Newton Method for Convex Composite Optimization","display_name":"Majorizing Functions and Convergence of the Gauss\u2013Newton Method for Convex Composite Optimization","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2025702035","doi":"https://doi.org/10.1137/06065622x","mag":"2025702035"},"language":"en","primary_location":{"id":"doi:10.1137/06065622x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06065622x","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/A5100424953","display_name":"Chong Li","orcid":"https://orcid.org/0000-0003-1910-155X"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chong Li","raw_affiliation_strings":["Zhejiang, University"],"affiliations":[{"raw_affiliation_string":"Zhejiang, University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040074886","display_name":"K. F. Ng","orcid":null},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"K. F. Ng","raw_affiliation_strings":["Department of Mathematics, Chinese University of Hong Kong, Hong Kong, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chinese University of Hong Kong, Hong Kong, P. R. China","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040074886"],"corresponding_institution_ids":["https://openalex.org/I177725633"],"apc_list":null,"apc_paid":null,"fwci":3.0481,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.90322581,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"18","issue":"2","first_page":"613","last_page":"642"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9993000030517578,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8528974056243896},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8022534251213074},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.5712882876396179},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5524498820304871},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5339345335960388},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5230458974838257},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4746328592300415},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45783212780952454},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.45383620262145996},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43088996410369873},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3475438356399536},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32607945799827576},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13423845171928406}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8528974056243896},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8022534251213074},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.5712882876396179},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5524498820304871},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5339345335960388},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5230458974838257},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4746328592300415},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45783212780952454},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.45383620262145996},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43088996410369873},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3475438356399536},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32607945799827576},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13423845171928406},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/06065622x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06065622x","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:10.1.1.162.2706","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.162.2706","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cuhk.edu.hk/~kfng/Lnkf6nR.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5799999833106995,"display_name":"Reduced inequalities"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322942","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48"},{"id":"https://openalex.org/F4320334924","display_name":"Program for New Century Excellent Talents in University","ror":"https://ror.org/01mv9t934"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1489887087","https://openalex.org/W1550563201","https://openalex.org/W1553702074","https://openalex.org/W1571614612","https://openalex.org/W1968363522","https://openalex.org/W1974251642","https://openalex.org/W1976487400","https://openalex.org/W1995457312","https://openalex.org/W2008832947","https://openalex.org/W2018508199","https://openalex.org/W2020708563","https://openalex.org/W2022034444","https://openalex.org/W2034171981","https://openalex.org/W2045056049","https://openalex.org/W2050766281","https://openalex.org/W2055883125","https://openalex.org/W2064694904","https://openalex.org/W2077658674","https://openalex.org/W2082725151","https://openalex.org/W2094683072","https://openalex.org/W2098003069","https://openalex.org/W2127838862","https://openalex.org/W2150200785","https://openalex.org/W2157170476","https://openalex.org/W3038830718"],"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":{"We":[0],"introduce":[1],"a":[2,19,37],"notion":[3],"of":[4,33,36,51,65],"quasi":[5],"regularity":[6],"for":[7,76],"points":[8,35],"with":[9],"respect":[10],"to":[11,26,59],"the":[12,31,47,55,61,69,77,88],"inclusion":[13],"$F(x)\\in":[14],"C$,":[15],"where":[16],"F":[17],"is":[18,30,91,95],"nonlinear":[20],"Fr\u00e9chet":[21],"differentiable":[22],"function":[23,40,57,80],"from":[24],"${\\mathbb{R}}^v$":[25],"${\\mathbb{R}}^m$.":[27],"When":[28],"C":[29],"set":[32],"minimum":[34],"convex":[38,78],"real-valued":[39],"h":[41],"on":[42],"${\\mathbb{R}}^m$":[43],"and":[44,93],"$F'$":[45,94],"satisfies":[46],"L-average":[48],"Lipschitz":[49],"condition":[50],"Wang,":[52],"we":[53],"use":[54],"majorizing":[56],"technique":[58],"establish":[60],"semilocal":[62],"linear/quadratic":[63],"convergence":[64],"sequences":[66],"generated":[67],"by":[68],"Gauss\u2013Newton":[70],"method":[71],"(with":[72],"quasi-regular":[73],"initial":[74,89],"points)":[75],"composite":[79],"$h\\circ":[81],"F$.":[82],"Results":[83],"are":[84],"new":[85],"even":[86],"when":[87],"point":[90],"regular":[92],"Lipschitz.":[96]},"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":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}