{"id":"https://openalex.org/W2964206681","doi":"https://doi.org/10.1137/16m1070463","title":"Relaxation and Purification for Nonconvex Variational Problems in Dual Banach Spaces: The Minimization Principle in Saturated Measure Spaces","display_name":"Relaxation and Purification for Nonconvex Variational Problems in Dual Banach Spaces: The Minimization Principle in Saturated Measure Spaces","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2964206681","doi":"https://doi.org/10.1137/16m1070463","mag":"2964206681"},"language":"en","primary_location":{"id":"doi:10.1137/16m1070463","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1070463","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and 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/A5040496706","display_name":"Nobusumi Sagara","orcid":"https://orcid.org/0000-0001-8049-2727"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nobusumi Sagara","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040496706"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.4159,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.94847575,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"55","issue":"5","first_page":"3154","last_page":"3170"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9944000244140625,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9653000235557556,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.8877257704734802},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7848550081253052},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.7120290398597717},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6157715320587158},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5990974307060242},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.49581584334373474},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4678274989128113},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4048677086830139},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3792356252670288},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3041708469390869}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8877257704734802},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7848550081253052},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.7120290398597717},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6157715320587158},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5990974307060242},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.49581584334373474},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4678274989128113},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4048677086830139},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3792356252670288},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3041708469390869},{"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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1070463","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1070463","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","score":0.4099999964237213,"display_name":"Decent work and economic growth"}],"awards":[{"id":"https://openalex.org/G4694468972","display_name":null,"funder_award_id":"26380246","funder_id":"https://openalex.org/F4320320912","funder_display_name":"Ministry of Education, Culture, Sports, Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320320912","display_name":"Ministry of Education, Culture, Sports, Science and Technology","ror":"https://ror.org/048rj2z13"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W63549402","https://openalex.org/W67402863","https://openalex.org/W1169993152","https://openalex.org/W1508357471","https://openalex.org/W1862423851","https://openalex.org/W1969853731","https://openalex.org/W1974214056","https://openalex.org/W1978385082","https://openalex.org/W1986368501","https://openalex.org/W1987385435","https://openalex.org/W2019657104","https://openalex.org/W2025057664","https://openalex.org/W2027074075","https://openalex.org/W2029301255","https://openalex.org/W2034922316","https://openalex.org/W2052333598","https://openalex.org/W2060122986","https://openalex.org/W2062531601","https://openalex.org/W2063981907","https://openalex.org/W2081684371","https://openalex.org/W2087392114","https://openalex.org/W2089406255","https://openalex.org/W2092661956","https://openalex.org/W2104831113","https://openalex.org/W2117572139","https://openalex.org/W2152872399","https://openalex.org/W2963017614"],"related_works":["https://openalex.org/W2278466645","https://openalex.org/W2170662346","https://openalex.org/W2368891994","https://openalex.org/W1988145293","https://openalex.org/W2092661520","https://openalex.org/W2122085706","https://openalex.org/W1992304457","https://openalex.org/W2053733287","https://openalex.org/W2593327172","https://openalex.org/W2962951952"],"abstract_inverted_index":{"We":[0,27,55],"formulate":[1],"bang-bang,":[2],"purification,":[3],"and":[4,14,78],"minimization":[5],"principles":[6],"in":[7],"dual":[8],"Banach":[9],"spaces":[10],"with":[11,39],"Gelfand":[12],"integrals":[13],"provide":[15],"a":[16,51,57,66],"complete":[17],"characterization":[18],"of":[19,23,32,46,59,69,87],"the":[20,33,44,73,76,85],"saturation":[21,74],"property":[22],"finite":[24,52],"measure":[25,53],"spaces.":[26],"also":[28],"present":[29],"an":[30],"application":[31],"relaxation":[34,77],"technique":[35],"to":[36,83],"large":[37,60],"economies":[38],"infinite-dimensional":[40],"commodity":[41],"spaces,":[42],"where":[43],"space":[45],"agents":[47],"is":[48,63],"modeled":[49],"as":[50,65],"space.":[54],"propose":[56],"\u201crelaxation\u201d":[58],"economies,":[61],"which":[62],"regarded":[64],"reasonable":[67],"convexification":[68],"original":[70],"economies.":[71],"Under":[72],"hypothesis,":[75],"purification":[79],"techniques":[80],"enable":[81],"us":[82],"prove":[84],"existence":[86],"Pareto":[88],"optimal":[89],"allocations":[90],"without":[91],"convexity":[92],"assumptions.":[93]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}