{"id":"https://openalex.org/W2346151177","doi":"https://doi.org/10.1080/10556788.2016.1178262","title":"On the differentiability check in gradient sampling methods","display_name":"On the differentiability check in gradient sampling methods","publication_year":2016,"publication_date":"2016-05-02","ids":{"openalex":"https://openalex.org/W2346151177","doi":"https://doi.org/10.1080/10556788.2016.1178262","mag":"2346151177"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2016.1178262","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2016.1178262","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://dx.doi.org/10.1080/10556788.2016.1178262","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071584113","display_name":"Elias S. Helou","orcid":"https://orcid.org/0000-0001-5157-3851"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]},{"id":"https://openalex.org/I4210131883","display_name":"Brazilian Society of Computational and Applied Mathematics","ror":"https://ror.org/03kcw4w74","country_code":"BR","type":"other","lineage":["https://openalex.org/I4210131883"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Elias Salom\u00e3o Helou","raw_affiliation_strings":["Institute of Mathematical Sciences and Computation, University of S\u00e3o Paulo, S\u00e3o Carlos, Brazil"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences and Computation, University of S\u00e3o Paulo, S\u00e3o Carlos, Brazil","institution_ids":["https://openalex.org/I4210131883","https://openalex.org/I17974374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029948617","display_name":"Sandra A. Santos","orcid":"https://orcid.org/0000-0002-6250-0137"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Sandra A. Santos","raw_affiliation_strings":["Department of Applied Mathematics, University of Campinas, Campinas, Brazil"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Campinas, Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074986936","display_name":"Lucas E. A. Sim\u00f5es","orcid":"https://orcid.org/0000-0002-2305-3565"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Lucas E. A. Sim\u00f5es","raw_affiliation_strings":["Department of Applied Mathematics, University of Campinas, Campinas, Brazil"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Campinas, Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071584113"],"corresponding_institution_ids":["https://openalex.org/I17974374","https://openalex.org/I4210131883"],"apc_list":null,"apc_paid":null,"fwci":2.7633,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.8879293,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"31","issue":"5","first_page":"983","last_page":"1007"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9979000091552734,"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":0.9979000091552734,"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":0.9966999888420105,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9882000088691711,"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/mathematics","display_name":"Mathematics","score":0.7765982747077942},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.7546157836914062},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.47354763746261597},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4286329746246338},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3763291835784912},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24059909582138062},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1473211944103241}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7765982747077942},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7546157836914062},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.47354763746261597},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4286329746246338},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3763291835784912},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24059909582138062},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1473211944103241},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/10556788.2016.1178262","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2016.1178262","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},{"id":"pmh:002762274","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1080/10556788.2016.1178262","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:002762274","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1080/10556788.2016.1178262","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"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":"reponame:Reposit\u00f3rio Institucional da USP (Biblioteca Digital da Produ\u00e7\u00e3o Intelectual)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2669988965","display_name":null,"funder_award_id":"2013&#x0002F;14615-7","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G3388712446","display_name":null,"funder_award_id":"2013/05475-7,2013/07375-0,2013/14615-7,2013/16508-3","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G5874346256","display_name":null,"funder_award_id":"304032/2010-7","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G8938818447","display_name":null,"funder_award_id":"304032&#x0002F;2010-7","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1031767768","https://openalex.org/W1551360398","https://openalex.org/W1984223686","https://openalex.org/W1985700739","https://openalex.org/W1992929347","https://openalex.org/W2000985550","https://openalex.org/W2015263936","https://openalex.org/W2026174223","https://openalex.org/W2064942524","https://openalex.org/W2071634839","https://openalex.org/W2079688774","https://openalex.org/W2084788303","https://openalex.org/W2088127528","https://openalex.org/W2100210445","https://openalex.org/W2151568819","https://openalex.org/W2167137033","https://openalex.org/W3106807711","https://openalex.org/W4211092921","https://openalex.org/W4212912562"],"related_works":["https://openalex.org/W2373677839","https://openalex.org/W972173259","https://openalex.org/W2787058745","https://openalex.org/W1970594704","https://openalex.org/W2331550167","https://openalex.org/W2321250155","https://openalex.org/W1983366713","https://openalex.org/W4212900149","https://openalex.org/W2332201812","https://openalex.org/W2909780748"],"abstract_inverted_index":{"The":[0],"present":[1],"study":[2],"aims":[3],"to":[4,111],"carefully":[5],"discuss":[6],"the":[7,13,23,31,37,48,51,55,58,61,75,80,83,102],"importance":[8],"of":[9,15,25,50,60,82],"differentiability":[10,52,76],"checks":[11],"during":[12],"execution":[14],"methods":[16],"based":[17],"on":[18],"gradient":[19],"sampling.":[20],"We":[21,40],"stress":[22],"significance":[24],"this":[26,68],"procedure":[27],"not":[28],"only":[29],"from":[30],"theoretical":[32,103],"perspective,":[33],"but":[34],"also":[35,108],"in":[36,54,86,89],"practical":[38],"implementation.":[39],"support":[41],"our":[42,105],"claims":[43],"exhibiting":[44],"illustrative":[45],"examples":[46],"where":[47],"absence":[49],"check":[53,77],"method":[56,84],"prevents":[57],"achievement":[59],"minimization":[62],"problem":[63],"solution.":[64],"As":[65],"possible":[66],"alternatives,":[67],"manuscript":[69],"presents":[70],"two":[71],"procedures":[72],"that":[73,100],"suppress":[74],"without":[78],"affecting":[79],"convergence":[81],"(both":[85],"theory":[87],"and":[88],"practice).":[90],"Lastly,":[91],"by":[92],"solving":[93],"a":[94],"difficult":[95],"control":[96],"problem,":[97],"we":[98],"show":[99],"besides":[101],"appeal":[104],"changes":[106],"may":[107],"be":[109],"useful":[110],"address":[112],"real":[113],"problems.":[114]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2016-06-24T00:00:00"}
