{"id":"https://openalex.org/W2089859140","doi":"https://doi.org/10.1137/130932934","title":"Gradient Type Optimization Methods For Electronic Structure Calculations","display_name":"Gradient Type Optimization Methods For Electronic Structure Calculations","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2089859140","doi":"https://doi.org/10.1137/130932934","mag":"2089859140"},"language":"en","primary_location":{"id":"doi:10.1137/130932934","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130932934","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/A5023021429","display_name":"Xin Zhang","orcid":"https://orcid.org/0000-0001-6649-1103"},"institutions":[{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]},{"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"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xin Zhang","raw_affiliation_strings":["Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210090176","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102388604","display_name":"Jinwei Zhu","orcid":"https://orcid.org/0009-0000-3707-8096"},"institutions":[{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]},{"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinwei Zhu","raw_affiliation_strings":["Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210090176","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006127137","display_name":"Zaiwen Wen","orcid":"https://orcid.org/0000-0003-1762-0671"},"institutions":[{"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/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zaiwen Wen","raw_affiliation_strings":["Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210090176","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113202217","display_name":"Aihui Zhou","orcid":null},"institutions":[{"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/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Aihui Zhou","raw_affiliation_strings":["Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210090176","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5023021429"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210090176"],"apc_list":null,"apc_paid":null,"fwci":3.6559,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.93311744,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"36","issue":"3","first_page":"C265","last_page":"C289"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9988999962806702,"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":0.9988999962806702,"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/T10083","display_name":"Graphene research and applications","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10382","display_name":"Quantum and electron transport phenomena","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6610658764839172},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6362425088882446},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6067596673965454},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5811213254928589},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5493915677070618},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.5402576327323914},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5379617214202881},{"id":"https://openalex.org/keywords/stiefel-manifold","display_name":"Stiefel manifold","score":0.5097798705101013},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.45257043838500977},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.443744957447052},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43878427147865295},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.4302976727485657},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4180070161819458},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4138650596141815},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2156851887702942},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20456480979919434},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19742479920387268},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0977843701839447}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6610658764839172},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6362425088882446},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6067596673965454},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5811213254928589},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5493915677070618},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.5402576327323914},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5379617214202881},{"id":"https://openalex.org/C612670","wikidata":"https://www.wikidata.org/wiki/Q7616373","display_name":"Stiefel manifold","level":2,"score":0.5097798705101013},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.45257043838500977},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.443744957447052},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43878427147865295},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4302976727485657},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4180070161819458},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4138650596141815},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2156851887702942},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20456480979919434},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19742479920387268},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0977843701839447},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/130932934","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130932934","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.765.545","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.765.545","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1308.2864.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W1544171083","https://openalex.org/W1804110266","https://openalex.org/W1966406013","https://openalex.org/W1968648081","https://openalex.org/W1969264669","https://openalex.org/W1969824929","https://openalex.org/W1975832162","https://openalex.org/W1980170509","https://openalex.org/W1985095956","https://openalex.org/W1986574273","https://openalex.org/W1995051821","https://openalex.org/W1998134546","https://openalex.org/W2003656569","https://openalex.org/W2007395042","https://openalex.org/W2009272335","https://openalex.org/W2011493730","https://openalex.org/W2013183108","https://openalex.org/W2015600650","https://openalex.org/W2018566483","https://openalex.org/W2020428152","https://openalex.org/W2032569130","https://openalex.org/W2038281434","https://openalex.org/W2039113872","https://openalex.org/W2039842735","https://openalex.org/W2045596260","https://openalex.org/W2048332510","https://openalex.org/W2048633871","https://openalex.org/W2049079467","https://openalex.org/W2051906496","https://openalex.org/W2052171888","https://openalex.org/W2058337926","https://openalex.org/W2064274879","https://openalex.org/W2066371837","https://openalex.org/W2066898005","https://openalex.org/W2069294211","https://openalex.org/W2070126925","https://openalex.org/W2071750684","https://openalex.org/W2073829819","https://openalex.org/W2076605490","https://openalex.org/W2078223384","https://openalex.org/W2084303191","https://openalex.org/W2086094876","https://openalex.org/W2086953401","https://openalex.org/W2091127828","https://openalex.org/W2092344142","https://openalex.org/W2093861682","https://openalex.org/W2094045530","https://openalex.org/W2098432400","https://openalex.org/W2106173883","https://openalex.org/W2124673426","https://openalex.org/W2129909514","https://openalex.org/W2156974254","https://openalex.org/W2160089699","https://openalex.org/W2161365734","https://openalex.org/W2162349032","https://openalex.org/W2170930163","https://openalex.org/W2230728100","https://openalex.org/W2501300253","https://openalex.org/W2990280590","https://openalex.org/W3101253177"],"related_works":["https://openalex.org/W3206955995","https://openalex.org/W2944517508","https://openalex.org/W4367692288","https://openalex.org/W4353007138","https://openalex.org/W3133127780","https://openalex.org/W3173103748","https://openalex.org/W2086698159","https://openalex.org/W4309210394","https://openalex.org/W4320473289","https://openalex.org/W2313335380"],"abstract_inverted_index":{"The":[0,22,140],"density":[1],"functional":[2,154,190],"theory":[3,117],"(DFT)":[4],"in":[5],"electronic":[6],"structure":[7],"calculations":[8],"can":[9,111,202],"be":[10,112],"formulated":[11],"as":[12,105,107,181,183],"either":[13],"a":[14,18,98],"nonlinear":[15],"eigenvalue":[16,134,172],"or":[17],"direct":[19,78],"minimization":[20,79],"problem.":[21],"most":[23],"widely":[24],"used":[25],"approach":[26],"for":[27,56,75,118,179],"solving":[28,57,76],"the":[29,32,43,58,77,86,89,115,130,148,151,159,162,165,184,187],"former":[30],"is":[31,41,47,128,136,195],"so-called":[33],"self-consistent":[34],"field":[35],"(SCF)":[36],"iteration.":[37],"A":[38,124],"common":[39],"observation":[40],"that":[42,129,200],"convergence":[44,54,93,96,109],"of":[45,132,143,150,186],"SCF":[46,65,204],"not":[48,62],"clear":[49],"theoretically,":[50],"while":[51],"approaches":[52,145],"with":[53,64],"guarantees":[55],"latter":[59],"are":[60,169,175],"often":[61,176],"competitive":[63],"numerically.":[66],"In":[67],"this":[68],"paper,":[69],"we":[70],"study":[71],"gradient":[72,87,119,157],"type":[73],"methods":[74,120],"problem":[80],"by":[81],"constructing":[82],"new":[83],"iterations":[84],"along":[85],"on":[88,121,158,206],"Stiefel":[90],"manifold.":[91,166],"Global":[92],"rate":[94,110],"(i.e.,":[95],"to":[97],"stationary":[99],"point":[100],"from":[101,114,147],"any":[102],"initial":[103],"solution)":[104],"well":[106],"local":[108],"obtained":[113],"standard":[116],"manifold":[122,160],"directly.":[123],"major":[125],"computational":[126],"advantage":[127],"computation":[131,173],"linear":[133],"problems":[135],"no":[137],"longer":[138],"needed.":[139],"main":[141],"costs":[142],"our":[144],"arise":[146],"assembling":[149],"total":[152,188],"energy":[153,189],"and":[155,161,174,191],"its":[156,192],"projection":[163],"onto":[164],"These":[167],"tasks":[168],"cheaper":[170],"than":[171],"more":[177],"suitable":[178],"parallelization":[180],"long":[182],"evaluation":[185],"partial":[193],"derivative":[194],"efficient.":[196],"Numerical":[197],"results":[198],"show":[199],"they":[201],"outperform":[203],"consistently":[205],"many":[207],"practical":[208],"large":[209],"systems.":[210]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-22T08:38:42.863108","created_date":"2025-10-10T00:00:00"}