{"id":"https://openalex.org/W2138238186","doi":"https://doi.org/10.1109/itwnit.2009.5158549","title":"On minimization of multivariate entropy functionals","display_name":"On minimization of multivariate entropy functionals","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2138238186","doi":"https://doi.org/10.1109/itwnit.2009.5158549","mag":"2138238186"},"language":"en","primary_location":{"id":"doi:10.1109/itwnit.2009.5158549","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itwnit.2009.5158549","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Information Theory Workshop on Networking and Information Theory","raw_type":"proceedings-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/A5026417214","display_name":"Imre Csisz\u00e1r","orcid":"https://orcid.org/0000-0003-1936-2012"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"id":"https://openalex.org/I198412221","display_name":"HUN-REN Institute for Nuclear Research","ror":"https://ror.org/006vxbq87","country_code":"HU","type":"facility","lineage":["https://openalex.org/I198412221","https://openalex.org/I4387152226"]},{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"government","lineage":["https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Imre Csiszar","raw_affiliation_strings":["A. R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences (ATOMKI), Budapest, Hungary","A. R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, H-1364 Budapest, P.O.Box 127, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"A. R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences (ATOMKI), Budapest, Hungary","institution_ids":["https://openalex.org/I127817813","https://openalex.org/I198412221","https://openalex.org/I7597260"]},{"raw_affiliation_string":"A. R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, H-1364 Budapest, P.O.Box 127, Hungary","institution_ids":["https://openalex.org/I7597260"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045494632","display_name":"Franti\u0161ek Mat\u00fa\u0161","orcid":"https://orcid.org/0000-0003-3113-9243"},"institutions":[{"id":"https://openalex.org/I202391551","display_name":"Czech Academy of Sciences","ror":"https://ror.org/053avzc18","country_code":"CZ","type":"government","lineage":["https://openalex.org/I202391551"]},{"id":"https://openalex.org/I4210119419","display_name":"Czech Academy of Sciences, Institute of Information Theory and Automation","ror":"https://ror.org/03h1hsz49","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210119419"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Frantisek Matus","raw_affiliation_strings":["Institute of Information Theory and Automation, Academy of Sciences\uc2a0of the\uc2a0Czech Republic, Prague, Czech Republic","Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, 18208 Prague, P.O.Box 18, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Information Theory and Automation, Academy of Sciences\uc2a0of the\uc2a0Czech Republic, Prague, Czech Republic","institution_ids":["https://openalex.org/I4210119419"]},{"raw_affiliation_string":"Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, 18208 Prague, P.O.Box 18, Czech Republic","institution_ids":["https://openalex.org/I202391551"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7482,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.93267882,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"8","issue":null,"first_page":"96","last_page":"100"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9911999702453613,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9901999831199646,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.7730934023857117},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6991212368011475},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.678534984588623},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6260967254638672},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6011292338371277},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5996028184890747},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5378953218460083},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.4902389645576477},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.4707180857658386},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4591159224510193},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4508056044578552},{"id":"https://openalex.org/keywords/entropy-maximization","display_name":"Entropy maximization","score":0.4445127248764038},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4216134548187256},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.35225987434387207},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20058810710906982},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13434499502182007},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0988483726978302},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06549772620201111}],"concepts":[{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.7730934023857117},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6991212368011475},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.678534984588623},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6260967254638672},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6011292338371277},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5996028184890747},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5378953218460083},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.4902389645576477},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.4707180857658386},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4591159224510193},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4508056044578552},{"id":"https://openalex.org/C127233936","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Entropy maximization","level":3,"score":0.4445127248764038},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4216134548187256},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.35225987434387207},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20058810710906982},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13434499502182007},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0988483726978302},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06549772620201111},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/itwnit.2009.5158549","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itwnit.2009.5158549","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Information Theory Workshop on Networking and Information Theory","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4099999964237213,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1535258871","https://openalex.org/W1685293311","https://openalex.org/W1919788179","https://openalex.org/W1989661300","https://openalex.org/W2033468335","https://openalex.org/W2098862199","https://openalex.org/W2104812799","https://openalex.org/W2142912299","https://openalex.org/W2159455062","https://openalex.org/W2163803752","https://openalex.org/W3193262203","https://openalex.org/W4249667877","https://openalex.org/W4388279027","https://openalex.org/W6684190412","https://openalex.org/W6831385702","https://openalex.org/W6858212420"],"related_works":["https://openalex.org/W2026600343","https://openalex.org/W2999421545","https://openalex.org/W2388570749","https://openalex.org/W2510140549","https://openalex.org/W4239678022","https://openalex.org/W2130502871","https://openalex.org/W4248569606","https://openalex.org/W2350695164","https://openalex.org/W2370594013","https://openalex.org/W2365171912"],"abstract_inverted_index":{"The":[0,31],"problem":[1],"of":[2,38],"minimizing":[3],"convex":[4,20,28],"integral":[5],"functionals":[6],"subject":[7],"to":[8,35],"moment-like":[9],"constraints":[10],"is":[11],"treated":[12],"in":[13,41],"a":[14],"general":[15],"setting":[16],"when":[17],"the":[18,36],"underlying":[19],"function":[21],"may":[22],"be":[23],"multivariate,":[24],"perhaps":[25],"not":[26],"strictly":[27],"or":[29],"differentiable.":[30],"results":[32],"are":[33],"applied":[34],"minimization":[37],"f-divergences":[39],"simultaneously":[40],"both":[42],"variables.":[43]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}