{"id":"https://openalex.org/W2026257541","doi":"https://doi.org/10.1515/1569395054069008","title":"A new class of memory gradient methods with inexact line searches","display_name":"A new class of memory gradient methods with inexact line searches","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2026257541","doi":"https://doi.org/10.1515/1569395054069008","mag":"2026257541"},"language":"en","primary_location":{"id":"doi:10.1515/1569395054069008","is_oa":false,"landing_page_url":"https://doi.org/10.1515/1569395054069008","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","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/A5088063385","display_name":"Zhang\u2010Jie Shi","orcid":"https://orcid.org/0000-0002-0919-752X"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Z.-J. Shi","raw_affiliation_strings":["College of Operations Research and Management, Qufu Normal University, Rizhao, Shandong 276826, P.R.China, and Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, P. R. China"],"affiliations":[{"raw_affiliation_string":"College of Operations Research and Management, Qufu Normal University, Rizhao, Shandong 276826, P.R.China, and Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, P. R. China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I202126657","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088063385"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I202126657","https://openalex.org/I4210120485"],"apc_list":null,"apc_paid":null,"fwci":0.8629,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.73540644,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"13","issue":"1","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":0.9997000098228455,"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":0.9997000098228455,"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":0.9926000237464905,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9847999811172485,"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/line-search","display_name":"Line search","score":0.8891829252243042},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.677699625492096},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.605014443397522},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5956057906150818},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.5896111130714417},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5544843673706055},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5525085926055908},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.5294173359870911},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5264989733695984},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43167683482170105},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36463481187820435},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1183224618434906},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.061058759689331055}],"concepts":[{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.8891829252243042},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.677699625492096},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.605014443397522},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5956057906150818},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.5896111130714417},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5544843673706055},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5525085926055908},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.5294173359870911},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5264989733695984},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43167683482170105},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36463481187820435},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1183224618434906},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.061058759689331055},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/1569395054069008","is_oa":false,"landing_page_url":"https://doi.org/10.1515/1569395054069008","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5099999904632568,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W194445265","https://openalex.org/W1669104078","https://openalex.org/W1976370770","https://openalex.org/W1982580180","https://openalex.org/W1984003452","https://openalex.org/W1984937277","https://openalex.org/W1991328835","https://openalex.org/W1993913013","https://openalex.org/W1996525837","https://openalex.org/W2001652206","https://openalex.org/W2039235927","https://openalex.org/W2051434435","https://openalex.org/W2054094588","https://openalex.org/W2056603712","https://openalex.org/W2079777091","https://openalex.org/W2081842231","https://openalex.org/W2084643483","https://openalex.org/W2088817878","https://openalex.org/W2108560279","https://openalex.org/W2118700449","https://openalex.org/W3029645440","https://openalex.org/W4285719527","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W2893613551","https://openalex.org/W2381924799","https://openalex.org/W2587204848","https://openalex.org/W2355555245","https://openalex.org/W2356977358","https://openalex.org/W2569220980","https://openalex.org/W2372778757","https://openalex.org/W2048029112","https://openalex.org/W2060820585","https://openalex.org/W2183734858"],"abstract_inverted_index":{"The":[0,18,59],"paper":[1],"presents":[2],"a":[3,30,40],"new":[4,50,78],"class":[5],"of":[6,62],"memory":[7],"gradient":[8],"methods":[9,19,27,51,64,87],"with":[10],"inexact":[11,35],"line":[12,36,85],"searches":[13,37],"for":[14],"unconstrained":[15,95],"minimization":[16,96],"problems.":[17,97],"use":[20,34],"more":[21,81],"previous":[22],"iterative":[23],"information":[24],"than":[25,83],"other":[26,84],"to":[28,38],"generate":[29],"search":[31,86],"direction":[32],"and":[33,88],"select":[39],"step-size":[41],"at":[42],"each":[43],"iteration.":[44],"It":[45],"is":[46,65],"proved":[47],"that":[48,76],"the":[49],"have":[52],"global":[53],"convergence":[54,60],"under":[55,68],"weak":[56],"mild":[57],"conditions.":[58],"rate":[61],"these":[63,77],"also":[66],"investigated":[67],"some":[69],"special":[70],"cases.":[71],"Some":[72],"numerical":[73],"experiments":[74],"show":[75],"algorithms":[79],"converge":[80],"stably":[82],"are":[89],"effective":[90],"in":[91],"solving":[92],"large":[93],"scale":[94]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-28T08:17:26.163206","created_date":"2025-10-10T00:00:00"}