{"id":"https://openalex.org/W2080183064","doi":"https://doi.org/10.4304/jsw.8.7.1568-1576","title":"A Semismooth Active-set Algorithm for Degenerate Nonlinear Complementarity Problems","display_name":"A Semismooth Active-set Algorithm for Degenerate Nonlinear Complementarity Problems","publication_year":2013,"publication_date":"2013-07-01","ids":{"openalex":"https://openalex.org/W2080183064","doi":"https://doi.org/10.4304/jsw.8.7.1568-1576","mag":"2080183064"},"language":"en","primary_location":{"id":"doi:10.4304/jsw.8.7.1568-1576","is_oa":false,"landing_page_url":"https://doi.org/10.4304/jsw.8.7.1568-1576","pdf_url":null,"source":{"id":"https://openalex.org/S114141714","display_name":"Journal of Software","issn_l":"1796-217X","issn":["1796-217X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318660","host_organization_name":"Academy Publisher","host_organization_lineage":["https://openalex.org/P4310318660"],"host_organization_lineage_names":["Academy Publisher"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Software","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/A5023003320","display_name":"Haodong Yu","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Haodong Yu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023003320"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1469675,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"7","first_page":null,"last_page":null},"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":0.9980000257492065,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9855999946594238,"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/computer-science","display_name":"Computer science","score":0.8261783123016357},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.7198542952537537},{"id":"https://openalex.org/keywords/mixed-complementarity-problem","display_name":"Mixed complementarity problem","score":0.6423317193984985},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5787044167518616},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4937931001186371},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4908807873725891},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.4827841520309448},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.454143762588501},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.14412707090377808},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.099610835313797}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8261783123016357},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.7198542952537537},{"id":"https://openalex.org/C77196050","wikidata":"https://www.wikidata.org/wiki/Q6883962","display_name":"Mixed complementarity problem","level":3,"score":0.6423317193984985},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5787044167518616},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4937931001186371},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4908807873725891},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.4827841520309448},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.454143762588501},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14412707090377808},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.099610835313797},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4304/jsw.8.7.1568-1576","is_oa":false,"landing_page_url":"https://doi.org/10.4304/jsw.8.7.1568-1576","pdf_url":null,"source":{"id":"https://openalex.org/S114141714","display_name":"Journal of Software","issn_l":"1796-217X","issn":["1796-217X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318660","host_organization_name":"Academy Publisher","host_organization_lineage":["https://openalex.org/P4310318660"],"host_organization_lineage_names":["Academy Publisher"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1551360398","https://openalex.org/W1985229624","https://openalex.org/W1993647205","https://openalex.org/W2040628347","https://openalex.org/W2046272803","https://openalex.org/W2050864977","https://openalex.org/W2069976088","https://openalex.org/W2087973298","https://openalex.org/W2090689930","https://openalex.org/W2128234186","https://openalex.org/W2138506796","https://openalex.org/W2147051624"],"related_works":["https://openalex.org/W2128234186","https://openalex.org/W2276648117","https://openalex.org/W2391525457","https://openalex.org/W2084792246","https://openalex.org/W819098253","https://openalex.org/W2085014864","https://openalex.org/W2350200292","https://openalex.org/W2374008704","https://openalex.org/W190854043","https://openalex.org/W157775922"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,59],"semismooth":[3],"active-set":[4,20],"Newton":[5],"algorithm":[6,57],"for":[7],"solving":[8],"the":[9,19,24,30,49,53,56,70,80,82,116,119],"nonlinear":[10],"complementarity":[11],"problems":[12],"with":[13],"degenerate":[14,25,83],"solutions.":[15],"This":[16,73],"method":[17,74],"introduces":[18],"technique":[21],"to":[22,47],"identify":[23],"set.":[26],"At":[27],"each":[28,98],"iteration,":[29],"search":[31],"direction":[32],"is":[33,63,95,107],"obtained":[34,108],"by":[35],"two":[36],"reduced":[37,92],"linear":[38,93],"systems.":[39],"Instead":[40],"of":[41,52,118],"employing":[42],"gradient":[43,67],"steps":[44],"as":[45,109],"adjustments":[46],"guarantee":[48],"sufficient":[50],"reduction":[51],"merit":[54],"function,":[55],"employs":[58],"Newton-type":[60],"direction,":[61,68],"which":[62],"more":[64],"efficient":[65],"than":[66],"in":[69],"adjustment":[71],"step.":[72],"has":[75],"globally":[76],"convergence.":[77],"When":[78],"near":[79],"solution,":[81],"set":[84],"will":[85],"be":[86],"identified":[87],"correctly,":[88],"and":[89],"only":[90],"one":[91],"system":[94],"solved":[96],"at":[97],"iteration.":[99],"Under":[100],"some":[101],"mild":[102],"assumptions,":[103],"locally":[104],"superlinear":[105],"convergence":[106],"well.":[110],"Numerical":[111],"experiments":[112],"on":[113],"MATLAB":[114],"shows":[115],"efficiency":[117],"method.":[120]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
