{"id":"https://openalex.org/W4410494969","doi":"https://doi.org/10.1287/moor.2023.0356","title":"Newton-CG Methods for Nonconvex Unconstrained Optimization with H\u00f6lder Continuous Hessian","display_name":"Newton-CG Methods for Nonconvex Unconstrained Optimization with H\u00f6lder Continuous Hessian","publication_year":2025,"publication_date":"2025-05-19","ids":{"openalex":"https://openalex.org/W4410494969","doi":"https://doi.org/10.1287/moor.2023.0356"},"language":"en","primary_location":{"id":"doi:10.1287/moor.2023.0356","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2023.0356","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://liu.diva-portal.org/smash/get/diva2:1963266/FULLTEXT01","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014605956","display_name":"C. He","orcid":"https://orcid.org/0000-0003-2402-3437"},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Chuan He","raw_affiliation_strings":["Department of Mathematics, Link\u00f6ping University, SE-581 83 Linkping, Sweden"],"raw_orcid":"https://orcid.org/0000-0003-2402-3437","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Link\u00f6ping University, SE-581 83 Linkping, Sweden","institution_ids":["https://openalex.org/I102134673"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060016795","display_name":"Heng Huang","orcid":"https://orcid.org/0000-0002-3483-8333"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Heng Huang","raw_affiliation_strings":["Department of Computer Science, University of Maryland, College Park, Maryland 20742"],"raw_orcid":"https://orcid.org/0000-0002-3483-8333","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Maryland, College Park, Maryland 20742","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000609407","display_name":"Zhaosong Lu","orcid":"https://orcid.org/0000-0003-3277-7853"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhaosong Lu","raw_affiliation_strings":["Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, Minnesota 55455"],"raw_orcid":"https://orcid.org/0000-0003-3277-7853","affiliations":[{"raw_affiliation_string":"Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, Minnesota 55455","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15742642,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"51","issue":"2","first_page":"1284","last_page":"1311"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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":0.9998000264167786,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.8619270324707031},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8303670883178711},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.704020619392395},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.6194341778755188},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.589963436126709},{"id":"https://openalex.org/keywords/h\u00f6lder-condition","display_name":"H\u00f6lder condition","score":0.5007703304290771},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.491430401802063},{"id":"https://openalex.org/keywords/hessian-equation","display_name":"Hessian equation","score":0.4407043159008026},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19593730568885803},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1293015480041504}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8619270324707031},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8303670883178711},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.704020619392395},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.6194341778755188},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.589963436126709},{"id":"https://openalex.org/C553313952","wikidata":"https://www.wikidata.org/wiki/Q1537963","display_name":"H\u00f6lder condition","level":2,"score":0.5007703304290771},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.491430401802063},{"id":"https://openalex.org/C73729460","wikidata":"https://www.wikidata.org/wiki/Q17023339","display_name":"Hessian equation","level":4,"score":0.4407043159008026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19593730568885803},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1293015480041504},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1287/moor.2023.0356","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2023.0356","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:DiVA.org:liu-214211","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-214211","pdf_url":"https://liu.diva-portal.org/smash/get/diva2:1963266/FULLTEXT01","source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:DiVA.org:liu-214211","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-214211","pdf_url":"https://liu.diva-portal.org/smash/get/diva2:1963266/FULLTEXT01","source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G18439693","display_name":"Collaborative Research: III: Medium: New Machine Learning Empowered Nanoinformatics System for Advancing Nanomaterial Design","funder_award_id":"2211491","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2644920612","display_name":null,"funder_award_id":"IIS-2211491","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6098521345","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8667467031","display_name":"Collaborative Research: III: Medium: New Machine Learning Empowered Nanoinformatics System for Advancing Nanomaterial Design","funder_award_id":"2347592","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410494969.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1985240368","https://openalex.org/W1994974865","https://openalex.org/W2006449495","https://openalex.org/W2009941369","https://openalex.org/W2033894760","https://openalex.org/W2040466831","https://openalex.org/W2156005216","https://openalex.org/W2398500126","https://openalex.org/W2530585400","https://openalex.org/W2546420264","https://openalex.org/W2599851351","https://openalex.org/W2623997598","https://openalex.org/W2962948705","https://openalex.org/W2963075511","https://openalex.org/W2963386167","https://openalex.org/W2963900797","https://openalex.org/W2964000362","https://openalex.org/W2971617498","https://openalex.org/W3021249612","https://openalex.org/W3126946265","https://openalex.org/W4385493863","https://openalex.org/W4399752055"],"related_works":["https://openalex.org/W1991833659","https://openalex.org/W2996136316","https://openalex.org/W2489086843","https://openalex.org/W19604512","https://openalex.org/W2983297293","https://openalex.org/W2023266244","https://openalex.org/W2015856668","https://openalex.org/W203338483","https://openalex.org/W2089895988","https://openalex.org/W2033626567"],"abstract_inverted_index":{"In":[0],"this":[1,39,70,95],"paper,":[2],"we":[3,21,50,98],"consider":[4],"a":[5,11,24,52,115],"nonconvex":[6],"unconstrained":[7],"optimization":[8],"problem":[9],"minimizing":[10],"twice":[12],"differentiable":[13],"objective":[14],"function":[15],"with":[16],"H\u00f6lder":[17,44],"continuous":[18],"Hessian.":[19],"Specifically,":[20],"first":[22,74],"propose":[23],"Newton-conjugate":[25],"gradient":[26],"(Newton-CG)":[27],"method":[28,55,71,77,113],"for":[29,85],"finding":[30,86],"an":[31,87],"approximate":[32,88],"first-":[33,89],"and":[34,82,90,133,140,177],"second-order":[35,76,91],"stationary":[36,92],"point":[37,93],"of":[38,61,67,94,109,172,182],"problem,":[40],"assuming":[41],"the":[42,65,73,79,105,128,138,151,164,170,178],"associated":[43],"parameters":[45],"are":[46],"explicitly":[47],"known.":[48],"Then,":[49],"develop":[51],"parameter-free":[53,75,111],"Newton-CG":[54,112],"without":[56],"requiring":[57],"any":[58],"prior":[59],"knowledge":[60],"these":[62],"parameters.":[63],"To":[64],"best":[66],"our":[68,110],"knowledge,":[69],"is":[72],"achieving":[78],"best-known":[80],"iteration":[81],"operation":[83],"complexity":[84],"problem.":[96],"Finally,":[97],"present":[99],"preliminary":[100],"numerical":[101],"results":[102],"to":[103],"demonstrate":[104],"superior":[106],"practical":[107],"performance":[108],"over":[114],"well-known":[116],"regularized":[117],"Newton":[118],"method.":[119],"Funding:":[120],"C.":[121],"He":[122],"was":[123,146,159],"partially":[124,147,160],"financially":[125,148,161],"supported":[126,149,162],"by":[127,137,150,163],"Wallenberg":[129,142],"AI,":[130],"Autonomous":[131],"Systems":[132],"Software":[134],"Program":[135],"funded":[136],"Knut":[139],"Alice":[141],"Foundation.":[143],"H.":[144],"Huang":[145],"National":[152,165],"Science":[153,166],"Foundation":[154,167],"[Award":[155,168,175,185],"IIS-2347592].":[156],"Z.":[157],"Lu":[158],"IIS-2211491],":[169],"Office":[171,181],"Naval":[173],"Research":[174,184],"N00014-24-1-2702],":[176],"Air":[179],"Force":[180],"Scientific":[183],"FA9550-24-1-0343].":[186]},"counts_by_year":[],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
