{"id":"https://openalex.org/W2033381781","doi":"https://doi.org/10.1137/060659739","title":"Explicit Solutions for a Class of Nonlinear PDEs that Arise in Allocation Problems","display_name":"Explicit Solutions for a Class of Nonlinear PDEs that Arise in Allocation Problems","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2033381781","doi":"https://doi.org/10.1137/060659739","mag":"2033381781"},"language":"en","primary_location":{"id":"doi:10.1137/060659739","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060659739","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5010647194","display_name":"Paul Dupuis","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Paul Dupuis","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091234933","display_name":"Jim X. Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jim X. Zhang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010647194"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14961848,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"39","issue":"5","first_page":"1627","last_page":"1667"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.984000027179718,"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":0.984000027179718,"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/T11898","display_name":"Economics of Agriculture and Food Markets","score":0.9435999989509583,"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/T10007","display_name":"Monetary Policy and Economic Impact","score":0.9431999921798706,"subfield":{"id":"https://openalex.org/subfields/2000","display_name":"General Economics, Econometrics and Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7998950481414795},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.7793859243392944},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5888898372650146},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.527497410774231},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5028743147850037},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4705546200275421},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4112653434276581},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1445048749446869},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10742413997650146}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7998950481414795},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7793859243392944},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5888898372650146},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.527497410774231},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5028743147850037},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4705546200275421},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4112653434276581},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1445048749446869},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10742413997650146},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/060659739","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060659739","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1567262822","https://openalex.org/W1970322545","https://openalex.org/W1975736346","https://openalex.org/W2021611402","https://openalex.org/W2023077134"],"related_works":["https://openalex.org/W2051058708","https://openalex.org/W154868527","https://openalex.org/W1494268238","https://openalex.org/W1983207144","https://openalex.org/W2490706771","https://openalex.org/W2480116122","https://openalex.org/W4255576661","https://openalex.org/W1516574938","https://openalex.org/W2563912921","https://openalex.org/W2087352669"],"abstract_inverted_index":{"To":[0],"exploit":[1],"large":[2,38],"deviation":[3,39],"approximations":[4],"for":[5,41,46,91],"allocation":[6,47,60],"and":[7,29,115],"occupancy":[8],"problems":[9,40,48,61],"one":[10,49,94],"must":[11],"solve":[12],"a":[13,20,70,74],"deterministic":[14],"optimal":[15],"control":[16],"problem":[17],"(or":[18],"equivalently,":[19],"calculus":[21],"of":[22,37,59,69,77,96,126,131],"variations":[23],"problem).":[24],"As":[25],"this":[26],"paper":[27],"demonstrates,":[28],"in":[30],"sharp":[31],"contrast":[32],"to":[33,138],"the":[34,103,109,117,127,132],"great":[35],"majority":[36],"processes":[42],"with":[43,73,136],"state":[44],"dependence,":[45],"can":[50],"construct":[51,113],"more":[52,92],"or":[53],"less":[54],"explicit":[55,121],"solutions.":[56],"Two":[57],"classes":[58],"are":[62],"studied.":[63],"The":[64,80,120],"first":[65],"class":[66,82],"considers":[67,83],"objects":[68],"single":[71],"type":[72,95],"parameterized":[75],"family":[76],"placement":[78,87],"probabilities.":[79],"second":[81],"only":[84],"equally":[85],"likely":[86],"probabilities":[88],"but":[89],"allows":[90],"than":[93],"object.":[97],"In":[98],"both":[99],"cases,":[100],"we":[101],"identify":[102,116],"Hamilton\u2013Jacobi\u2013Bellman":[104],"equation,":[105],"whose":[106],"solution":[107],"characterizes":[108],"minimal":[110],"cost,":[111],"explicitly":[112],"solutions,":[114],"minimizing":[118],"trajectories.":[119],"construction":[122],"is":[123],"possible":[124],"because":[125],"very":[128],"tractable":[129],"properties":[130],"relative":[133],"entropy":[134],"function":[135],"respect":[137],"optimization.":[139]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
