{"id":"https://openalex.org/W2151898625","doi":"https://doi.org/10.1137/050635225","title":"A New Active Set Algorithm for Box Constrained Optimization","display_name":"A New Active Set Algorithm for Box Constrained Optimization","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2151898625","doi":"https://doi.org/10.1137/050635225","mag":"2151898625"},"language":"en","primary_location":{"id":"doi:10.1137/050635225","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050635225","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/A5002362913","display_name":"William W. Hager","orcid":"https://orcid.org/0000-0003-3132-7017"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"William W. Hager","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101893795","display_name":"Hongchao Zhang","orcid":"https://orcid.org/0000-0003-2518-6975"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hongchao Zhang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002362913"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.3287,"has_fulltext":false,"cited_by_count":253,"citation_normalized_percentile":{"value":0.99246799,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"17","issue":"2","first_page":"526","last_page":"557"},"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9927999973297119,"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/stationary-point","display_name":"Stationary point","score":0.6693293452262878},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.653052806854248},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.6325073838233948},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6138667464256287},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5800681710243225},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5408483147621155},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5078433156013489},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.49828481674194336},{"id":"https://openalex.org/keywords/feasible-region","display_name":"Feasible region","score":0.42864465713500977},{"id":"https://openalex.org/keywords/constrained-optimization","display_name":"Constrained optimization","score":0.4282801151275635},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.42231547832489014},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2540794610977173}],"concepts":[{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.6693293452262878},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.653052806854248},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.6325073838233948},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6138667464256287},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5800681710243225},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5408483147621155},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5078433156013489},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.49828481674194336},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.42864465713500977},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.4282801151275635},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.42231547832489014},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2540794610977173},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050635225","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050635225","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":85,"referenced_works":["https://openalex.org/W20194637","https://openalex.org/W59491134","https://openalex.org/W89654658","https://openalex.org/W102551087","https://openalex.org/W124158035","https://openalex.org/W147998453","https://openalex.org/W1497361805","https://openalex.org/W1499828147","https://openalex.org/W1546266651","https://openalex.org/W1546275378","https://openalex.org/W1563835996","https://openalex.org/W1592657385","https://openalex.org/W1967077838","https://openalex.org/W1968553199","https://openalex.org/W1973431552","https://openalex.org/W1973734200","https://openalex.org/W1976831027","https://openalex.org/W1978100686","https://openalex.org/W1979382551","https://openalex.org/W1980940812","https://openalex.org/W1986822694","https://openalex.org/W1991907403","https://openalex.org/W1993647205","https://openalex.org/W1994015146","https://openalex.org/W1994603587","https://openalex.org/W2000218110","https://openalex.org/W2000359198","https://openalex.org/W2005126631","https://openalex.org/W2005660297","https://openalex.org/W2008063657","https://openalex.org/W2012121807","https://openalex.org/W2012341322","https://openalex.org/W2012766316","https://openalex.org/W2013243898","https://openalex.org/W2014739921","https://openalex.org/W2014851363","https://openalex.org/W2015530812","https://openalex.org/W2016518303","https://openalex.org/W2018215034","https://openalex.org/W2024441306","https://openalex.org/W2026289804","https://openalex.org/W2027791819","https://openalex.org/W2031127394","https://openalex.org/W2035741312","https://openalex.org/W2040006905","https://openalex.org/W2041523977","https://openalex.org/W2042613327","https://openalex.org/W2043430160","https://openalex.org/W2044106880","https://openalex.org/W2049470252","https://openalex.org/W2052782332","https://openalex.org/W2054295574","https://openalex.org/W2057667075","https://openalex.org/W2062042185","https://openalex.org/W2063677971","https://openalex.org/W2066205820","https://openalex.org/W2069053817","https://openalex.org/W2070784012","https://openalex.org/W2071467620","https://openalex.org/W2076605490","https://openalex.org/W2078283558","https://openalex.org/W2083431695","https://openalex.org/W2084123115","https://openalex.org/W2088241859","https://openalex.org/W2089333839","https://openalex.org/W2092285919","https://openalex.org/W2094960695","https://openalex.org/W2098132613","https://openalex.org/W2118075667","https://openalex.org/W2123028442","https://openalex.org/W2132347401","https://openalex.org/W2144331407","https://openalex.org/W2148589597","https://openalex.org/W2149454052","https://openalex.org/W2162988958","https://openalex.org/W2163392119","https://openalex.org/W2167137033","https://openalex.org/W2733179301","https://openalex.org/W2798766386","https://openalex.org/W2808829785","https://openalex.org/W2898826383","https://openalex.org/W2985272081","https://openalex.org/W4240823076","https://openalex.org/W4253878268","https://openalex.org/W4254755288"],"related_works":["https://openalex.org/W2604655597","https://openalex.org/W2846499288","https://openalex.org/W2360314603","https://openalex.org/W3082608044","https://openalex.org/W2357791884","https://openalex.org/W4229957265","https://openalex.org/W2393400400","https://openalex.org/W4291138102","https://openalex.org/W2015399832","https://openalex.org/W3092127437"],"abstract_inverted_index":{"An":[0],"active":[1],"set":[2,26],"algorithm":[3,12,49,72,96,108],"(ASA)":[4],"for":[5,29,58,97,110],"box":[6,118],"constrained":[7,119],"optimization":[8,22,54,77],"is":[9,41,86],"developed.":[10],"The":[11],"consists":[13],"of":[14,27,83],"a":[15,25,38,44,59],"nonmonotone":[16],"gradient":[17,99,107],"projection":[18,100],"step,":[19,23],"an":[20],"unconstrained":[21,53,76,111],"and":[24,102,124],"rules":[28],"branching":[30],"between":[31],"the":[32,48,64,71,84,90,98,103,122],"two":[33],"steps.":[34],"Global":[35],"convergence":[36],"to":[37,52,75],"stationary":[39,46,61],"point":[40],"established.":[42],"For":[43],"nondegenerate":[45],"point,":[47,62],"eventually":[50,73],"reduces":[51,74],"without":[55,78],"restarts.":[56,79],"Similarly,":[57],"degenerate":[60],"where":[63],"strong":[65],"second\u2010order":[66],"sufficient":[67],"optimality":[68],"condition":[69],"holds,":[70],"A":[80],"specific":[81],"implementation":[82],"ASA":[85],"given":[87],"which":[88],"exploits":[89],"recently":[91,104],"developed":[92,105],"cyclic":[93],"Barzilai\u2013Borwein":[94],"(CBB)":[95],"step":[101],"conjugate":[106],"CG_DESCENT":[109],"optimization.":[112],"Numerical":[113],"experiments":[114],"are":[115],"presented":[116],"using":[117],"problems":[120],"in":[121],"CUTEr":[123],"MINPACK\u20102":[125],"test":[126],"problem":[127],"libraries.":[128]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":15},{"year":2016,"cited_by_count":23},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":15},{"year":2012,"cited_by_count":19}],"updated_date":"2026-03-29T08:15:47.926485","created_date":"2025-10-10T00:00:00"}