{"id":"https://openalex.org/W4383065888","doi":"https://doi.org/10.1007/s11590-023-02033-5","title":"Detecting negative eigenvalues of exact and approximate Hessian matrices in optimization","display_name":"Detecting negative eigenvalues of exact and approximate Hessian matrices in optimization","publication_year":2023,"publication_date":"2023-07-04","ids":{"openalex":"https://openalex.org/W4383065888","doi":"https://doi.org/10.1007/s11590-023-02033-5"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-023-02033-5","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1007/s11590-023-02033-5","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","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/A5068401790","display_name":"Warren Hare","orcid":"https://orcid.org/0000-0002-4240-3903"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]},{"id":"https://openalex.org/I4405260628","display_name":"University of British Columbia, Okanagan Campus","ror":"https://ror.org/04241wz75","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490","https://openalex.org/I4405260628"]},{"id":"https://openalex.org/I822440","display_name":"Okanagan University College","ror":"https://ror.org/02mxmh518","country_code":"CA","type":"education","lineage":["https://openalex.org/I822440"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Warren Hare","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, Okanagan Campus, Kelowna, BC, V1V1V7, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Okanagan Campus, Kelowna, BC, V1V1V7, Canada","institution_ids":["https://openalex.org/I822440","https://openalex.org/I141945490","https://openalex.org/I4405260628"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024675306","display_name":"Cl\u00e9ment W. Royer","orcid":"https://orcid.org/0000-0003-2452-2172"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Cl\u00e9ment W. Royer","raw_affiliation_strings":["LAMSADE, CNRS, Universit\u00e9 Paris Dauphine-PSL, Place du Mar\u00e9chal de Lattre de Tassigny, Paris, 75016, France"],"raw_orcid":"https://orcid.org/0000-0003-2452-2172","affiliations":[{"raw_affiliation_string":"LAMSADE, CNRS, Universit\u00e9 Paris Dauphine-PSL, Place du Mar\u00e9chal de Lattre de Tassigny, Paris, 75016, France","institution_ids":["https://openalex.org/I56435720","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024675306","https://openalex.org/A5068401790"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I141945490","https://openalex.org/I4405260628","https://openalex.org/I56435720","https://openalex.org/I822440"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.3363,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.64198021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"17","issue":"8","first_page":"1739","last_page":"1756"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9994999766349792,"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":0.9993000030517578,"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":0.9977999925613403,"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/hessian-matrix","display_name":"Hessian matrix","score":0.9810893535614014},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7420239448547363},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.6834376454353333},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5665464997291565},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5640318393707275},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5624116659164429},{"id":"https://openalex.org/keywords/hessian-equation","display_name":"Hessian equation","score":0.5421889424324036},{"id":"https://openalex.org/keywords/quasi-newton-method","display_name":"Quasi-Newton method","score":0.49772027134895325},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4819793105125427},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48196718096733093},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.47456246614456177},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4545724093914032},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.4100596010684967},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3396631181240082},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3265530467033386},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.21627184748649597},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16538158059120178},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08100852370262146}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.9810893535614014},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7420239448547363},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.6834376454353333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5665464997291565},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5640318393707275},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5624116659164429},{"id":"https://openalex.org/C73729460","wikidata":"https://www.wikidata.org/wiki/Q17023339","display_name":"Hessian equation","level":4,"score":0.5421889424324036},{"id":"https://openalex.org/C114954040","wikidata":"https://www.wikidata.org/wiki/Q1476018","display_name":"Quasi-Newton method","level":4,"score":0.49772027134895325},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4819793105125427},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48196718096733093},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.47456246614456177},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4545724093914032},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.4100596010684967},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3396631181240082},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3265530467033386},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.21627184748649597},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16538158059120178},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08100852370262146},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11590-023-02033-5","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1007/s11590-023-02033-5","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04334269v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04334269","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Optimization Letters, 2023, 17, pp.1739-1756. ⟨10.1007/s11590-023-02033-5⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4261462415","display_name":null,"funder_award_id":"2018-03865","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W181733065","https://openalex.org/W1580352598","https://openalex.org/W1984488466","https://openalex.org/W2039665200","https://openalex.org/W2057565823","https://openalex.org/W2059125718","https://openalex.org/W2059586807","https://openalex.org/W2066494975","https://openalex.org/W2068484625","https://openalex.org/W2082877410","https://openalex.org/W2116007667","https://openalex.org/W2167511885","https://openalex.org/W2336146308","https://openalex.org/W2775085189","https://openalex.org/W2892093336","https://openalex.org/W2962881194","https://openalex.org/W2963075511","https://openalex.org/W6820434291"],"related_works":["https://openalex.org/W1991833659","https://openalex.org/W2023266244","https://openalex.org/W203338483","https://openalex.org/W19604512","https://openalex.org/W2015856668","https://openalex.org/W2033626567","https://openalex.org/W1977452077","https://openalex.org/W2089895988","https://openalex.org/W2083194257","https://openalex.org/W4383065888"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}