{"id":"https://openalex.org/W3048234810","doi":"https://doi.org/10.1007/s10107-020-01550-w","title":"Determination of convex functions via subgradients of minimal norm","display_name":"Determination of convex functions via subgradients of minimal norm","publication_year":2020,"publication_date":"2020-08-06","ids":{"openalex":"https://openalex.org/W3048234810","doi":"https://doi.org/10.1007/s10107-020-01550-w","mag":"3048234810"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-020-01550-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-020-01550-w","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://repositorio.uchile.cl/handle/2250/177278","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044297986","display_name":"Pedro P\u00e9rez-Aros","orcid":"https://orcid.org/0000-0002-8756-3011"},"institutions":[{"id":"https://openalex.org/I4210144665","display_name":"University of O'Higgins","ror":"https://ror.org/044cse639","country_code":"CL","type":"education","lineage":["https://openalex.org/I4210144665"]}],"countries":["CL"],"is_corresponding":true,"raw_author_name":"Pedro P\u00e9rez-Aros","raw_affiliation_strings":["Instituto de Ciencias de la Ingenier\u00eda, Universidad de O\u2019Higgins, Av. Libertador Bernardo O\u2019Higgins 611, Rancagua, Chile","Instituto de Ciencias de la Ingenier\u00eda, Universidad de O'Higgins, Av. Libertador Bernardo O'Higgins 611, Rancagua, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Ciencias de la Ingenier\u00eda, Universidad de O\u2019Higgins, Av. Libertador Bernardo O\u2019Higgins 611, Rancagua, Chile","institution_ids":["https://openalex.org/I4210144665"]},{"raw_affiliation_string":"Instituto de Ciencias de la Ingenier\u00eda, Universidad de O'Higgins, Av. Libertador Bernardo O'Higgins 611, Rancagua, Chile","institution_ids":["https://openalex.org/I4210144665"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047978518","display_name":"David Salas","orcid":"https://orcid.org/0000-0003-3924-366X"},"institutions":[{"id":"https://openalex.org/I4210144665","display_name":"University of O'Higgins","ror":"https://ror.org/044cse639","country_code":"CL","type":"education","lineage":["https://openalex.org/I4210144665"]},{"id":"https://openalex.org/I69737025","display_name":"University of Chile","ror":"https://ror.org/047gc3g35","country_code":"CL","type":"education","lineage":["https://openalex.org/I69737025"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"David Salas","raw_affiliation_strings":["Centro de Modelamiento Matem\u00e1tico, CNRS-UMI 2807, Universidad de Chile, Av. Beauchef 851, Santiago, Chile","Instituto de Ciencias de la Ingenier\u00eda, Universidad de O\u2019Higgins, Av. Libertador Bernardo O\u2019Higgins 611, Rancagua, Chile","Instituto de Ciencias de la Ingenier\u00eda, Universidad de O'Higgins, Av. Libertador Bernardo O'Higgins 611, Rancagua, Chile"],"raw_orcid":"https://orcid.org/0000-0003-3924-366X","affiliations":[{"raw_affiliation_string":"Centro de Modelamiento Matem\u00e1tico, CNRS-UMI 2807, Universidad de Chile, Av. Beauchef 851, Santiago, Chile","institution_ids":["https://openalex.org/I69737025"]},{"raw_affiliation_string":"Instituto de Ciencias de la Ingenier\u00eda, Universidad de O\u2019Higgins, Av. Libertador Bernardo O\u2019Higgins 611, Rancagua, Chile","institution_ids":["https://openalex.org/I4210144665"]},{"raw_affiliation_string":"Instituto de Ciencias de la Ingenier\u00eda, Universidad de O'Higgins, Av. Libertador Bernardo O'Higgins 611, Rancagua, Chile","institution_ids":["https://openalex.org/I4210144665"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003500683","display_name":"Emilio Vilches","orcid":"https://orcid.org/0000-0002-4387-9313"},"institutions":[{"id":"https://openalex.org/I4210144665","display_name":"University of O'Higgins","ror":"https://ror.org/044cse639","country_code":"CL","type":"education","lineage":["https://openalex.org/I4210144665"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Emilio Vilches","raw_affiliation_strings":["Instituto de Ciencias de la Ingenier\u00eda, Universidad de O\u2019Higgins, Av. Libertador Bernardo O\u2019Higgins 611, Rancagua, Chile","Instituto de Ciencias de la Ingenier\u00eda, Universidad de O'Higgins, Av. Libertador Bernardo O'Higgins 611, Rancagua, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Ciencias de la Ingenier\u00eda, Universidad de O\u2019Higgins, Av. Libertador Bernardo O\u2019Higgins 611, Rancagua, Chile","institution_ids":["https://openalex.org/I4210144665"]},{"raw_affiliation_string":"Instituto de Ciencias de la Ingenier\u00eda, Universidad de O'Higgins, Av. Libertador Bernardo O'Higgins 611, Rancagua, Chile","institution_ids":["https://openalex.org/I4210144665"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044297986"],"corresponding_institution_ids":["https://openalex.org/I4210144665"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.7226,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.76933816,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"190","issue":"1-2","first_page":"561","last_page":"583"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9976000189781189,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9976000189781189,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9818999767303467,"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/mathematics","display_name":"Mathematics","score":0.8803377151489258},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7346459627151489},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6133993864059448},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5985360741615295},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.5288169384002686},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5197746157646179},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4943861961364746},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.46874573826789856},{"id":"https://openalex.org/keywords/convex-domain","display_name":"Convex domain","score":0.4611200988292694},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4548453092575073},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4212414026260376},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.36781054735183716},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3598330616950989},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3583065867424011},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.288727343082428},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07685491442680359},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06488931179046631}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8803377151489258},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7346459627151489},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6133993864059448},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5985360741615295},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.5288169384002686},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5197746157646179},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4943861961364746},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.46874573826789856},{"id":"https://openalex.org/C2991999034","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex domain","level":3,"score":0.4611200988292694},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4548453092575073},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4212414026260376},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.36781054735183716},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3598330616950989},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3583065867424011},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.288727343082428},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07685491442680359},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06488931179046631},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-020-01550-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-020-01550-w","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:repositorio.uchile.cl:2250/177278","is_oa":true,"landing_page_url":"https://repositorio.uchile.cl/handle/2250/177278","pdf_url":null,"source":{"id":"https://openalex.org/S4306481413","display_name":"Universidad de Chile","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Programming","raw_type":"Art\u00edculo de revista"}],"best_oa_location":{"id":"pmh:oai:repositorio.uchile.cl:2250/177278","is_oa":true,"landing_page_url":"https://repositorio.uchile.cl/handle/2250/177278","pdf_url":null,"source":{"id":"https://openalex.org/S4306481413","display_name":"Universidad de Chile","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Programming","raw_type":"Art\u00edculo de revista"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G129531123","display_name":null,"funder_award_id":"1190110","funder_id":"https://openalex.org/F4320338106","funder_display_name":"Fondo de Fomento al Desarrollo Cient\u00edfico y Tecnol\u00f3gico"},{"id":"https://openalex.org/G6422802813","display_name":null,"funder_award_id":"3190229","funder_id":"https://openalex.org/F4320338106","funder_display_name":"Fondo de Fomento al Desarrollo Cient\u00edfico y Tecnol\u00f3gico"},{"id":"https://openalex.org/G8040557986","display_name":null,"funder_award_id":"11180098","funder_id":"https://openalex.org/F4320338106","funder_display_name":"Fondo de Fomento al Desarrollo Cient\u00edfico y Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320338106","display_name":"Fondo de Fomento al Desarrollo Cient\u00edfico y Tecnol\u00f3gico","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W110970250","https://openalex.org/W205960364","https://openalex.org/W1492700492","https://openalex.org/W1497246097","https://openalex.org/W1522579744","https://openalex.org/W1582617215","https://openalex.org/W1827780528","https://openalex.org/W1891854070","https://openalex.org/W1953936588","https://openalex.org/W1993207994","https://openalex.org/W1997852431","https://openalex.org/W2016456744","https://openalex.org/W2017413125","https://openalex.org/W2067243588","https://openalex.org/W2079488098","https://openalex.org/W2081798995","https://openalex.org/W2121562066","https://openalex.org/W2138867475","https://openalex.org/W2139691799","https://openalex.org/W2167897175","https://openalex.org/W2403704162","https://openalex.org/W2766276860","https://openalex.org/W2788021380","https://openalex.org/W2937565258","https://openalex.org/W2947900750","https://openalex.org/W2963070522","https://openalex.org/W2964210434","https://openalex.org/W3203406682","https://openalex.org/W4236384742","https://openalex.org/W4254573138","https://openalex.org/W4302408205","https://openalex.org/W4303084602"],"related_works":["https://openalex.org/W2007576447","https://openalex.org/W2137493863","https://openalex.org/W2356261519","https://openalex.org/W2379359887","https://openalex.org/W2185500298","https://openalex.org/W3199288759","https://openalex.org/W2026600343","https://openalex.org/W2040676043","https://openalex.org/W2051968184","https://openalex.org/W2510140549"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
