{"id":"https://openalex.org/W2513236568","doi":"https://doi.org/10.1137/15m104075x","title":"Nonlinear Preconditioning Techniques for Full-Space Lagrange--Newton Solution of PDE-Constrained Optimization Problems","display_name":"Nonlinear Preconditioning Techniques for Full-Space Lagrange--Newton Solution of PDE-Constrained Optimization Problems","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2513236568","doi":"https://doi.org/10.1137/15m104075x","mag":"2513236568"},"language":"en","primary_location":{"id":"doi:10.1137/15m104075x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m104075x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5109978591","display_name":"Haijian Yang","orcid":"https://orcid.org/0000-0001-7304-1282"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haijian Yang","raw_affiliation_strings":["Hunan University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hunan University","institution_ids":["https://openalex.org/I16609230"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067761186","display_name":"Feng\u2010Nan Hwang","orcid":"https://orcid.org/0000-0002-2012-3257"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Feng-Nan Hwang","raw_affiliation_strings":["Department of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006367748","display_name":"Xiao\u2010Chuan Cai","orcid":"https://orcid.org/0000-0003-0296-8640"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]},{"id":"https://openalex.org/I2802236040","display_name":"University of Colorado System","ror":"https://ror.org/00jc20583","country_code":"US","type":"education","lineage":["https://openalex.org/I2802236040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiao-Chuan Cai","raw_affiliation_strings":["University of Colorado Boulder"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Colorado Boulder","institution_ids":["https://openalex.org/I2802236040","https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.0463,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.95567761,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"38","issue":"5","first_page":"A2756","last_page":"A2778"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9980999827384949,"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":0.7684041261672974},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.7510722875595093},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.7009131908416748},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6524674296379089},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.6275280117988586},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5795726180076599},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4990816116333008},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.4567112326622009},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4498906135559082},{"id":"https://openalex.org/keywords/constraint-algorithm","display_name":"Constraint algorithm","score":0.4215860068798065},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4090909957885742},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.321329802274704}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7684041261672974},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.7510722875595093},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.7009131908416748},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6524674296379089},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.6275280117988586},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5795726180076599},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4990816116333008},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.4567112326622009},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4498906135559082},{"id":"https://openalex.org/C15980293","wikidata":"https://www.wikidata.org/wiki/Q5164368","display_name":"Constraint algorithm","level":3,"score":0.4215860068798065},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4090909957885742},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.321329802274704},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m104075x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m104075x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G139733092","display_name":null,"funder_award_id":"CCF-1216314","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6243979168","display_name":null,"funder_award_id":"91530103","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7097560840","display_name":null,"funder_award_id":"91330111","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8070665063","display_name":"\u975e\u7ebf\u6027\u533a\u57df\u5206\u89e3\u9884\u6761\u4ef6\u5b50\u7814\u7a76\u53ca\u5176\u5728\u6d41\u56fa\u8026\u5408\u63a7\u5236\u4e2d\u7684\u5e94\u7528","funder_award_id":"11571100","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8477354057","display_name":null,"funder_award_id":"MOST-103-2115-M-008-007","funder_id":"https://openalex.org/F4320322795","funder_display_name":"Ministry of Science and Technology, Taiwan"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322795","display_name":"Ministry of Science and Technology, Taiwan","ror":"https://ror.org/02kv4zf79"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W166999289","https://openalex.org/W1428340059","https://openalex.org/W1490416103","https://openalex.org/W1506342804","https://openalex.org/W1566323605","https://openalex.org/W1919576760","https://openalex.org/W1973254632","https://openalex.org/W1988588696","https://openalex.org/W1995371856","https://openalex.org/W1995561370","https://openalex.org/W2006651269","https://openalex.org/W2017345249","https://openalex.org/W2022772783","https://openalex.org/W2029670554","https://openalex.org/W2039641833","https://openalex.org/W2050255334","https://openalex.org/W2054026842","https://openalex.org/W2054921147","https://openalex.org/W2057231518","https://openalex.org/W2057576183","https://openalex.org/W2060949683","https://openalex.org/W2060985152","https://openalex.org/W2068484625","https://openalex.org/W2068696746","https://openalex.org/W2070656412","https://openalex.org/W2075087492","https://openalex.org/W2079440004","https://openalex.org/W2084073638","https://openalex.org/W2091515296","https://openalex.org/W2095751072","https://openalex.org/W2120494006","https://openalex.org/W2123029817","https://openalex.org/W2126906098","https://openalex.org/W2130756427","https://openalex.org/W2141870784","https://openalex.org/W2143628714","https://openalex.org/W2152023749","https://openalex.org/W2163114495","https://openalex.org/W2169562629","https://openalex.org/W2170489872","https://openalex.org/W2171303908","https://openalex.org/W2414175575","https://openalex.org/W3102441626","https://openalex.org/W3209210654"],"related_works":["https://openalex.org/W2024837890","https://openalex.org/W1979241556","https://openalex.org/W2074745806","https://openalex.org/W2021667451","https://openalex.org/W2352028553","https://openalex.org/W1967449934","https://openalex.org/W1970808271","https://openalex.org/W2045861968","https://openalex.org/W2017306930","https://openalex.org/W2781111882"],"abstract_inverted_index":{"The":[0,83,103],"full-space":[1],"Lagrange--Newton":[2],"algorithm":[3,75],"is":[4,34,50,119],"one":[5],"of":[6,44,80,100,109,150],"the":[7,29,32,42,62,77,98,101,110,117,130,146,151],"numerical":[8,140],"algorithms":[9],"for":[10,37,76],"solving":[11],"problems":[12,16],"arising":[13],"from":[14],"optimization":[15],"constrained":[17],"by":[18],"nonlinear":[19,104],"partial":[20],"differential":[21],"equations.":[22],"Newton-type":[23],"methods":[24],"enjoy":[25],"fast":[26],"convergence":[27,49],"when":[28,127],"nonlinearity":[30,99,118],"in":[31,61,97],"system":[33,84],"well-balanced;":[35],"however,":[36],"some":[38,108],"problems,":[39],"such":[40],"as":[41,114],"control":[43,79],"incompressible":[45,81],"flows,":[46],"even":[47],"linear":[48],"difficult":[51],"to":[52,129,144],"achieve":[53],"and":[54,89,113,121,148],"a":[55,70,94,115],"long":[56],"stagnation":[57],"period":[58],"often":[59],"appears":[60],"iteration":[63],"history.":[64],"In":[65],"this":[66],"work,":[67],"we":[68],"introduce":[69],"nonlinearly":[71],"preconditioned":[72],"inexact":[73,122,132],"Newton":[74,123,133],"boundary":[78],"flows.":[82],"has":[85],"nine":[86],"field":[87,91,111],"variables,":[88,112],"each":[90],"variable":[92],"plays":[93],"different":[95],"role":[96],"system.":[102],"preconditioner":[105],"approximately":[106],"removes":[107],"result,":[116],"balanced":[120],"converges":[124],"much":[125],"faster":[126],"compared":[128],"unpreconditioned":[131],"method":[134],"or":[135],"its":[136],"two-grid":[137],"version.":[138],"Some":[139],"results":[141],"are":[142],"presented":[143],"demonstrate":[145],"robustness":[147],"efficiency":[149],"algorithm.":[152]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
