{"id":"https://openalex.org/W1967759264","doi":"https://doi.org/10.1090/s0025-5718-98-00932-6","title":"Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities","display_name":"Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1967759264","doi":"https://doi.org/10.1090/s0025-5718-98-00932-6","mag":"1967759264"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-98-00932-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00932-6","pdf_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00932-6/S0025-5718-98-00932-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00932-6/S0025-5718-98-00932-6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100369445","display_name":"Xiaojun Chen","orcid":"https://orcid.org/0000-0002-6627-2637"},"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":"X. Chen","raw_affiliation_strings":["School of Mathematics The University of New South Wales Sydney 2052, Australia","School of Mathematics, The University of New South Wales, Sydney 2052, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics The University of New South Wales Sydney 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Mathematics, The University of New South Wales, Sydney 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011886900","display_name":"Liqun Qi","orcid":"https://orcid.org/0000-0002-1112-5250"},"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":"L. Qi","raw_affiliation_strings":["School of Mathematics The University of New South Wales Sydney 2052, Australia","School of Mathematics, The University of New South Wales, Sydney 2052, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics The University of New South Wales Sydney 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Mathematics, The University of New South Wales, Sydney 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029911976","display_name":"Defeng Sun","orcid":"https://orcid.org/0000-0003-0481-272X"},"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":"D. Sun","raw_affiliation_strings":["School of Mathematics The University of New South Wales Sydney 2052, Australia","School of Mathematics, The University of New South Wales, Sydney 2052, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics The University of New South Wales Sydney 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Mathematics, The University of New South Wales, Sydney 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":null,"apc_paid":null,"fwci":18.1665,"has_fulltext":true,"cited_by_count":287,"citation_normalized_percentile":{"value":0.9942832,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"67","issue":"222","first_page":"519","last_page":"540"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9973000288009644,"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":0.995199978351593,"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/algorithm","display_name":"Algorithm","score":0.7339744567871094},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.4355650544166565},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.4305034279823303},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4218444228172302},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42105263471603394},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39481353759765625},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3875841796398163},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1658531129360199}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7339744567871094},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.4355650544166565},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.4305034279823303},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4218444228172302},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42105263471603394},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39481353759765625},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3875841796398163},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1658531129360199},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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":4,"locations":[{"id":"doi:10.1090/s0025-5718-98-00932-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00932-6","pdf_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00932-6/S0025-5718-98-00932-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.145.8394","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.145.8394","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/1998-67-222/S0025-5718-98-00932-6/S0025-5718-98-00932-6.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.307.7392","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.307.7392","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/CQS_98.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.52.7530","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.7530","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.unsw.edu.au/~chen/bvi.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-98-00932-6","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-00932-6","pdf_url":"https://www.ams.org/mcom/1998-67-222/S0025-5718-98-00932-6/S0025-5718-98-00932-6.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.550000011920929,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1967759264.pdf","grobid_xml":"https://content.openalex.org/works/W1967759264.grobid-xml"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W19099988","https://openalex.org/W84287112","https://openalex.org/W104144503","https://openalex.org/W189973867","https://openalex.org/W261384220","https://openalex.org/W1529720318","https://openalex.org/W1551360398","https://openalex.org/W1564612581","https://openalex.org/W1599532185","https://openalex.org/W1604665355","https://openalex.org/W1970551061","https://openalex.org/W1972034149","https://openalex.org/W1977117914","https://openalex.org/W1980614749","https://openalex.org/W1981947863","https://openalex.org/W1982027431","https://openalex.org/W1990823216","https://openalex.org/W1992688650","https://openalex.org/W1995583003","https://openalex.org/W1997671037","https://openalex.org/W2001024683","https://openalex.org/W2005148680","https://openalex.org/W2007753746","https://openalex.org/W2009885647","https://openalex.org/W2019727142","https://openalex.org/W2036930530","https://openalex.org/W2037095211","https://openalex.org/W2053643774","https://openalex.org/W2056254398","https://openalex.org/W2057074226","https://openalex.org/W2069734325","https://openalex.org/W2070890393","https://openalex.org/W2084288112","https://openalex.org/W2087136707","https://openalex.org/W2088055586","https://openalex.org/W2088057743","https://openalex.org/W2088550353","https://openalex.org/W2090689930","https://openalex.org/W2090963365","https://openalex.org/W2092855431","https://openalex.org/W2093246563","https://openalex.org/W2105207928","https://openalex.org/W2113734366","https://openalex.org/W2151902790","https://openalex.org/W2166161964","https://openalex.org/W2290441346","https://openalex.org/W2478091498","https://openalex.org/W2971350920","https://openalex.org/W4206956014","https://openalex.org/W4211027407","https://openalex.org/W4247685432","https://openalex.org/W4285719527","https://openalex.org/W4299512035","https://openalex.org/W6727170356"],"related_works":["https://openalex.org/W1892467659","https://openalex.org/W1529400504","https://openalex.org/W2349865494","https://openalex.org/W2998403542","https://openalex.org/W2808586768","https://openalex.org/W2372553222","https://openalex.org/W3157620392","https://openalex.org/W2925832130","https://openalex.org/W2045715842","https://openalex.org/W2105880240"],"abstract_inverted_index":{"The":[0,210],"smoothing":[1,62,213,216,233,328],"Newton":[2,207,217,234,329],"method":[3,235,330],"for":[4,298],"solving":[5],"a":[6,58,99,273],"system":[7],"of":[8,60,145,212,337],"nonsmooth":[9,81],"equations":[10],"<inline-formula":[11,66,83,102,146,186,241,260,308],"content-type=\"math/mathml\">":[12,67,84,103,147,187,242,261,309],"<mml:math":[13,68,85,104,148,188,243,262,310],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[14,69,86,105,149,189,244,263,311],"alttext=\"upper":[15,87,245,312],"F":[16],"left-parenthesis":[17,107,151],"x":[18],"right-parenthesis":[19],"equals":[20],"0\">":[21],"<mml:semantics>":[22,71,89,115,159,193,247,265,314],"<mml:mrow>":[23,116,160],"<mml:mi>F</mml:mi>":[24,90,248],"<mml:mo":[25,28,118,130,162,174],"stretchy=\"false\">(</mml:mo>":[26,119,163],"<mml:mi>x</mml:mi>":[27,195],"stretchy=\"false\">)</mml:mo>":[29,131,175],"<mml:mo>=</mml:mo>":[30],"<mml:mn>0</mml:mn>":[31],"</mml:mrow>":[32,132,176],"<mml:annotation":[33,73,91,133,177,198,249,267,316],"encoding=\"application/x-tex\">F(x)=0</mml:annotation>":[34],"</mml:semantics>":[35,75,93,138,182,200,251,269,318],"</mml:math>":[36,76,94,139,183,201,252,270,319],"</inline-formula>":[37,77,95,140,184,202,253,271,320],",":[38,135,141,179],"which":[39],"may":[40],"arise":[41],"from":[42],"the":[43,47,61,65,80,143,206,232,257,286,304,322,327,334,338],"nonlinear":[44],"complementarity":[45],"problem,":[46],"variational":[48,301],"inequality":[49],"problem":[50,339],"or":[51],"other":[52],"problems,":[53],"can":[54],"be":[55],"regarded":[56],"as":[57,205,285],"variant":[59],"method.":[63],"At":[64],"alttext=\"k\">":[70],"<mml:mi>k</mml:mi>":[72,128,172,196],"encoding=\"application/x-tex\">k</mml:annotation>":[74],"th":[78],"step,":[79],"function":[82,101,306],"F\">":[88,246],"encoding=\"application/x-tex\">F</mml:annotation>":[92,250],"is":[96,203,236,254,307],"approximated":[97],"by":[98,326],"smooth":[100,282],"alttext=\"f":[106,150],"dot":[108,152],"comma":[109,153],"epsilon":[110,154],"Subscript":[111,155],"k":[112,156],"Baseline":[113,157],"right-parenthesis\">":[114,158],"<mml:mi>f</mml:mi>":[117,161,266],"<mml:mo>":[120,164],"\u22c5":[121,165],"</mml:mo>":[122,166],"<mml:mo>,</mml:mo>":[123,167],"<mml:msub>":[124,168],"<mml:mi>":[125,169],"\u03b5":[126,170],"</mml:mi>":[127,171],"</mml:msub>":[129,173],"encoding=\"application/x-tex\">f(\\cdot":[134,178],"\\varepsilon":[136,180],"_k)</mml:annotation>":[137,181],"and":[142,215,222,259,341],"derivative":[144],"at":[185,256],"alttext=\"x":[190],"Superscript":[191],"k\">":[192],"<mml:msup>":[194],"</mml:msup>":[197],"encoding=\"application/x-tex\">x^k</mml:annotation>":[199],"used":[204],"iterative":[208],"matrix.":[209],"merits":[211],"methods":[214,218],"are":[219],"global":[220],"convergence":[221],"convenience":[223],"in":[224],"handling.":[225],"In":[226],"this":[227,290],"paper,":[228],"we":[229,295],"show":[230,278,296],"that":[231,279,297],"also":[237],"superlinearly":[238,342],"convergent":[239],"if":[240,303],"semismooth":[255],"solution":[258,336],"alttext=\"f\">":[264],"encoding=\"application/x-tex\">f</mml:annotation>":[268],"satisfies":[272],"Jacobian":[274],"consistency":[275],"property.":[276,291],"We":[277],"most":[280],"common":[281],"functions,":[283],"such":[284],"Gabriel-Mor\u00e9":[287],"function,":[288],"have":[289],"As":[292],"an":[293],"application,":[294],"box":[299],"constrained":[300],"inequalities":[302],"involved":[305],"P\">":[313],"<mml:mi>P</mml:mi>":[315],"encoding=\"application/x-tex\">P</mml:annotation>":[317],"\u2013uniform,":[321],"iteration":[323],"sequence":[324],"generated":[325],"will":[331],"converge":[332],"to":[333],"unique":[335],"globally":[340],"(quadratically).":[343]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":11}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
