{"id":"https://openalex.org/W3175130380","doi":"https://doi.org/10.1007/978-3-030-77957-3_11","title":"Quasiconvex Jensen Divergences and Quasiconvex Bregman Divergences","display_name":"Quasiconvex Jensen Divergences and Quasiconvex Bregman Divergences","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3175130380","doi":"https://doi.org/10.1007/978-3-030-77957-3_11","mag":"3175130380"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-77957-3_11","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-77957-3_11","pdf_url":null,"source":{"id":"https://openalex.org/S4210180650","display_name":"Springer proceedings in mathematics & statistics","issn_l":"2194-1009","issn":["2194-1009","2194-1017"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319972","host_organization_name":"Springer International Publishing","host_organization_lineage":["https://openalex.org/P4310319972","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer International Publishing","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Springer Proceedings in Mathematics & Statistics","raw_type":"book-chapter"},"type":"book-chapter","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/A5061293973","display_name":"Frank Nielsen","orcid":"https://orcid.org/0000-0001-5728-0726"},"institutions":[{"id":"https://openalex.org/I4210122684","display_name":"Sony Computer Science Laboratories","ror":"https://ror.org/02nc46417","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210122684"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Frank Nielsen","raw_affiliation_strings":["Sony Computer Science Laboratories Inc., Tokyo, Japan"],"raw_orcid":"https://orcid.org/0000-0001-5728-0726","affiliations":[{"raw_affiliation_string":"Sony Computer Science Laboratories Inc., Tokyo, Japan","institution_ids":["https://openalex.org/I4210122684"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051522702","display_name":"Ga\u00ebtan Hadjeres","orcid":"https://orcid.org/0000-0003-1462-6103"},"institutions":[{"id":"https://openalex.org/I4210131385","display_name":"Sony (France)","ror":"https://ror.org/03cr99w51","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210131385","https://openalex.org/I4210143797"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ga\u00ebtan Hadjeres","raw_affiliation_strings":["Sony Computer Science Laboratories, Paris, France"],"raw_orcid":"https://orcid.org/0000-0003-1462-6103","affiliations":[{"raw_affiliation_string":"Sony Computer Science Laboratories, Paris, France","institution_ids":["https://openalex.org/I4210131385"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061293973"],"corresponding_institution_ids":["https://openalex.org/I4210122684"],"apc_list":null,"apc_paid":null,"fwci":0.958,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.75608782,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"196","last_page":"218"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.977400004863739,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.977400004863739,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9656000137329102,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quasiconvex-function","display_name":"Quasiconvex function","score":0.9925521612167358},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6884375810623169},{"id":"https://openalex.org/keywords/bregman-divergence","display_name":"Bregman divergence","score":0.6545562744140625},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.48128002882003784},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.4452385902404785},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4419630169868469},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.42891326546669006},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.42679375410079956},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.41565704345703125},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3815152049064636},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3721907138824463},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32437461614608765},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.15941551327705383},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.0962655246257782},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06443971395492554}],"concepts":[{"id":"https://openalex.org/C80278974","wikidata":"https://www.wikidata.org/wiki/Q1126412","display_name":"Quasiconvex function","level":5,"score":0.9925521612167358},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6884375810623169},{"id":"https://openalex.org/C149073432","wikidata":"https://www.wikidata.org/wiki/Q4960382","display_name":"Bregman divergence","level":2,"score":0.6545562744140625},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.48128002882003784},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.4452385902404785},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4419630169868469},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.42891326546669006},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.42679375410079956},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.41565704345703125},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3815152049064636},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3721907138824463},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32437461614608765},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.15941551327705383},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0962655246257782},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06443971395492554},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-030-77957-3_11","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-77957-3_11","pdf_url":null,"source":{"id":"https://openalex.org/S4210180650","display_name":"Springer proceedings in mathematics & statistics","issn_l":"2194-1009","issn":["2194-1009","2194-1017"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319972","host_organization_name":"Springer International Publishing","host_organization_lineage":["https://openalex.org/P4310319972","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer International Publishing","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Springer Proceedings in Mathematics & Statistics","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W152055444","https://openalex.org/W1494379901","https://openalex.org/W1506313179","https://openalex.org/W1556911442","https://openalex.org/W1954793731","https://openalex.org/W1993087762","https://openalex.org/W1998932465","https://openalex.org/W2033468335","https://openalex.org/W2041512436","https://openalex.org/W2042799324","https://openalex.org/W2092898962","https://openalex.org/W2095456658","https://openalex.org/W2096765209","https://openalex.org/W2099111195","https://openalex.org/W2099531205","https://openalex.org/W2102714712","https://openalex.org/W2110861437","https://openalex.org/W2140505738","https://openalex.org/W2142433650","https://openalex.org/W2146355224","https://openalex.org/W2149607218","https://openalex.org/W2162995444","https://openalex.org/W2296319761","https://openalex.org/W2399052269","https://openalex.org/W2472357683","https://openalex.org/W2485135680","https://openalex.org/W2490754630","https://openalex.org/W2578335925","https://openalex.org/W2587048717","https://openalex.org/W2623585316","https://openalex.org/W2904160524","https://openalex.org/W2929620509","https://openalex.org/W2949613959","https://openalex.org/W2949979820","https://openalex.org/W2964046333","https://openalex.org/W3037943248","https://openalex.org/W3102206498","https://openalex.org/W3104653941","https://openalex.org/W3105985631","https://openalex.org/W4231019034","https://openalex.org/W4231410305","https://openalex.org/W4250589301","https://openalex.org/W6689075165"],"related_works":["https://openalex.org/W2522923325","https://openalex.org/W2169519573","https://openalex.org/W136137658","https://openalex.org/W4226270436","https://openalex.org/W2101504640","https://openalex.org/W2043483408","https://openalex.org/W2181909002","https://openalex.org/W2057676055","https://openalex.org/W2023539147","https://openalex.org/W3044808105"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}