{"id":"https://openalex.org/W2163991032","doi":"https://doi.org/10.1137/050638308","title":"Monge Property and Bounding Multivariate Probability Distribution Functions with Given Marginals and Covariances","display_name":"Monge Property and Bounding Multivariate Probability Distribution Functions with Given Marginals and Covariances","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2163991032","doi":"https://doi.org/10.1137/050638308","mag":"2163991032"},"language":"en","primary_location":{"id":"doi:10.1137/050638308","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050638308","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","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/A5021138723","display_name":"Xiaoling Hou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaoling Hou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056572859","display_name":"Andr\u00e1s Pr\u00e9kopa","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andr\u00e1s Pr\u00e9kopa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7775,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.78922023,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"18","issue":"1","first_page":"138","last_page":"155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9994000196456909,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9994000196456909,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.982699990272522,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.9176387190818787},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.6789078712463379},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.668229341506958},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6636512875556946},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.5466764569282532},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5248006582260132},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5202206969261169},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5069218277931213},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4803287088871002},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4326801300048828},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33245962858200073},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14354899525642395},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07247850298881531}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9176387190818787},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.6789078712463379},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.668229341506958},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6636512875556946},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.5466764569282532},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5248006582260132},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5202206969261169},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5069218277931213},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4803287088871002},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4326801300048828},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33245962858200073},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14354899525642395},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07247850298881531},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050638308","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050638308","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.160.1000","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.160.1000","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://rutcor.rutgers.edu/pub/rrr/reports2005/27_2005.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W159391839","https://openalex.org/W260397477","https://openalex.org/W1991863159","https://openalex.org/W2013345559","https://openalex.org/W2023878014","https://openalex.org/W2043641066","https://openalex.org/W2105016507","https://openalex.org/W2128817474","https://openalex.org/W2170698268","https://openalex.org/W2254463431","https://openalex.org/W2798344481","https://openalex.org/W2800137643","https://openalex.org/W3106992008","https://openalex.org/W3149766375"],"related_works":["https://openalex.org/W2049578243","https://openalex.org/W1828158523","https://openalex.org/W2122079181","https://openalex.org/W2000145235","https://openalex.org/W1985848810","https://openalex.org/W2889939530","https://openalex.org/W2399195672","https://openalex.org/W3121881699","https://openalex.org/W3120030401","https://openalex.org/W2748838164"],"abstract_inverted_index":{"Multivariate":[0],"probability":[1],"distributions":[2],"with":[3,9,48],"given":[4,68],"marginals":[5,116],"are":[6,22,51,67,106,127],"considered,":[7],"along":[8],"linear":[10,58],"functionals,":[11],"to":[12,24],"be":[13,40],"minimized":[14],"or":[15,28,31],"maximized,":[16],"acting":[17],"on":[18,84],"them.":[19],"The":[20],"functionals":[21],"supposed":[23],"satisfy":[25],"the":[26,70,80,85,98,109,114,119,122],"Monge":[27,30,49],"inverse":[29],"some":[32,88],"higher":[33],"order":[34],"convexity":[35],"property,":[36],"and":[37,53,64,92,100],"they":[38],"may":[39],"only":[41,113],"partially":[42],"known.":[43,128],"Existing":[44],"results":[45],"in":[46,55],"connection":[47],"arrays":[50],"reformulated":[52],"extended":[54],"terms":[56],"of":[57,79,87,121,124],"programming":[59],"dual":[60,89,103],"feasible":[61,90,104],"bases.":[62],"Lower":[63],"upper":[65],"bounds":[66],"for":[69,76,108],"optimum":[71],"value":[72],"as":[73,75],"well":[74],"unknown":[77],"coefficients":[78],"objective":[81,94],"function,":[82],"based":[83],"knowledge":[86],"bases":[91,105],"corresponding":[93],"function":[95],"coefficients.":[96],"In":[97],"two\u2010":[99],"three\u2010dimensional":[101],"cases":[102],"obtained":[107],"problem,":[110],"where":[111],"not":[112],"univariate":[115],"but":[117],"also":[118],"covariances":[120],"pairs":[123],"random":[125],"variables":[126]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}