{"id":"https://openalex.org/W2162057287","doi":"https://doi.org/10.1002/(sici)1099-1506(199805/06)5:3<219::aid-nla134>3.0.co;2-7","title":"Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems","display_name":"Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems","publication_year":1998,"publication_date":"1998-05-01","ids":{"openalex":"https://openalex.org/W2162057287","doi":"https://doi.org/10.1002/(sici)1099-1506(199805/06)5:3<219::aid-nla134>3.0.co;2-7","mag":"2162057287"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1099-1506(199805/06)5:3<219::aid-nla134>3.0.co;2-7","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199805/06)5:3<219::aid-nla134>3.0.co;2-7","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","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/A5073380305","display_name":"Ladislav Luk\u0161an","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119419","display_name":"Czech Academy of Sciences, Institute of Information Theory and Automation","ror":"https://ror.org/03h1hsz49","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210119419"]},{"id":"https://openalex.org/I4210155092","display_name":"Czech Academy of Sciences, Institute of Computer Science","ror":"https://ror.org/0496n6574","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210155092"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Ladislav Luk\u0161an","raw_affiliation_strings":["Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod voda\u0301renskou ve\u030cz\u030ci\u0301 2, 182 07 Prague 8, Czech Republic","Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod\u00e1renskou v\u011b\u017e\u00ed 2, 182 07 Prague 8, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod voda\u0301renskou ve\u030cz\u030ci\u0301 2, 182 07 Prague 8, Czech Republic","institution_ids":["https://openalex.org/I4210155092","https://openalex.org/I4210119419"]},{"raw_affiliation_string":"Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod\u00e1renskou v\u011b\u017e\u00ed 2, 182 07 Prague 8, Czech Republic","institution_ids":["https://openalex.org/I4210155092"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101963302","display_name":"Jan Vl\u010dek","orcid":"https://orcid.org/0000-0002-5870-3732"},"institutions":[{"id":"https://openalex.org/I4210155092","display_name":"Czech Academy of Sciences, Institute of Computer Science","ror":"https://ror.org/0496n6574","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210155092"]},{"id":"https://openalex.org/I4210119419","display_name":"Czech Academy of Sciences, Institute of Information Theory and Automation","ror":"https://ror.org/03h1hsz49","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210119419"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Jan Vl\u010dek","raw_affiliation_strings":["Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod voda\u0301renskou ve\u030cz\u030ci\u0301 2, 182 07 Prague 8, Czech Republic","Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod\u00e1renskou v\u011b\u017e\u00ed 2, 182 07 Prague 8, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod voda\u0301renskou ve\u030cz\u030ci\u0301 2, 182 07 Prague 8, Czech Republic","institution_ids":["https://openalex.org/I4210155092","https://openalex.org/I4210119419"]},{"raw_affiliation_string":"Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vod\u00e1renskou v\u011b\u017e\u00ed 2, 182 07 Prague 8, Czech Republic","institution_ids":["https://openalex.org/I4210155092"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073380305"],"corresponding_institution_ids":["https://openalex.org/I4210119419","https://openalex.org/I4210155092"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":3.9266,"has_fulltext":false,"cited_by_count":123,"citation_normalized_percentile":{"value":0.94315886,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"5","issue":"3","first_page":"219","last_page":"247"},"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":0.9990000128746033,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983999729156494,"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/preconditioner","display_name":"Preconditioner","score":0.8314136266708374},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.7570203542709351},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7520548701286316},{"id":"https://openalex.org/keywords/newtons-method-in-optimization","display_name":"Newton's method in optimization","score":0.6972371935844421},{"id":"https://openalex.org/keywords/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.6871955394744873},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.6087828278541565},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5312449932098389},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5171915292739868},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.4979419708251953},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.478519082069397},{"id":"https://openalex.org/keywords/coordinate-descent","display_name":"Coordinate descent","score":0.47145017981529236},{"id":"https://openalex.org/keywords/descent-direction","display_name":"Descent direction","score":0.4503615200519562},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.43826204538345337},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4238091707229614},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38753753900527954},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.3358818292617798},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.29715317487716675},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.2428552806377411},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2183200716972351},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09058520197868347}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8314136266708374},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.7570203542709351},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7520548701286316},{"id":"https://openalex.org/C179127668","wikidata":"https://www.wikidata.org/wiki/Q17086396","display_name":"Newton's method in optimization","level":4,"score":0.6972371935844421},{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.6871955394744873},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.6087828278541565},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5312449932098389},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5171915292739868},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.4979419708251953},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.478519082069397},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.47145017981529236},{"id":"https://openalex.org/C116149140","wikidata":"https://www.wikidata.org/wiki/Q2070951","display_name":"Descent direction","level":4,"score":0.4503615200519562},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.43826204538345337},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4238091707229614},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38753753900527954},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3358818292617798},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.29715317487716675},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.2428552806377411},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2183200716972351},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09058520197868347},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1099-1506(199805/06)5:3<219::aid-nla134>3.0.co;2-7","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199805/06)5:3<219::aid-nla134>3.0.co;2-7","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W89281171","https://openalex.org/W263597469","https://openalex.org/W1748199557","https://openalex.org/W1976222070","https://openalex.org/W1988796619","https://openalex.org/W2002352627","https://openalex.org/W2030855527","https://openalex.org/W2056723044","https://openalex.org/W2077658674","https://openalex.org/W2090356812","https://openalex.org/W2106353864","https://openalex.org/W2107501462","https://openalex.org/W2132421833","https://openalex.org/W2135959058","https://openalex.org/W2140803189","https://openalex.org/W3012317737","https://openalex.org/W4212997115","https://openalex.org/W6603622378","https://openalex.org/W6609720646","https://openalex.org/W6669838086","https://openalex.org/W6821904898"],"related_works":["https://openalex.org/W1585779400","https://openalex.org/W2015399832","https://openalex.org/W125730541","https://openalex.org/W2124959855","https://openalex.org/W4300813936","https://openalex.org/W4301973148","https://openalex.org/W2963332075","https://openalex.org/W2264498574","https://openalex.org/W2042185988","https://openalex.org/W2497192389"],"abstract_inverted_index":{"An":[0],"inexact":[1,100],"Newton":[2,101],"algorithm":[3,15],"for":[4,40],"large":[5,117],"sparse":[6],"equality":[7],"constrained":[8],"non-linear":[9],"programming":[10],"problems":[11],"is":[12,16,47,112],"proposed.":[13],"This":[14],"based":[17],"on":[18],"an":[19],"indefinitely":[20],"preconditioned":[21],"smoothed":[22],"conjugate":[23],"gradient":[24],"method":[25],"applied":[26],"to":[27,49,72],"the":[28,50,53,64,73,99],"linear":[29],"KKT":[30],"system":[31],"and":[32,62,70,90,110],"uses":[33],"a":[34,76,105,116],"simple":[35],"augmented":[36],"Lagrangian":[37],"merit":[38],"function":[39],"Armijo":[41],"type":[42],"stepsize":[43],"selection.":[44],"Most":[45],"attention":[46],"devoted":[48],"termination":[51],"of":[52,66,75,98,107,119],"CG":[54,68],"method,":[55],"guaranteeing":[56],"sufficient":[57],"descent":[58],"in":[59],"every":[60],"iteration":[61],"decreasing":[63],"number":[65],"required":[67],"iterations,":[69],"especially,":[71],"choice":[74],"suitable":[77],"preconditioner.":[78],"We":[79],"investigate":[80],"four":[81],"preconditioners,":[82],"which":[83],"have":[84],"2":[85,87],"\u00d7":[86],"block":[88],"structure,":[89],"prove":[91],"theoretically":[92],"their":[93],"good":[94],"properties.":[95],"The":[96],"efficiency":[97],"algorithm,":[102],"together":[103],"with":[104],"comparison":[106],"various":[108],"preconditioners":[109],"strategies,":[111],"demonstrated":[113],"by":[114],"using":[115],"collection":[118],"test":[120],"problems.":[121],"\u00a9":[122],"1998":[123],"John":[124],"Wiley":[125],"&":[126],"Sons,":[127],"Ltd.":[128]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":9}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
