{"id":"https://openalex.org/W1997543272","doi":"https://doi.org/10.1109/acc.2014.6859159","title":"A MCMC/Bernstein approach to chance constrained programs","display_name":"A MCMC/Bernstein approach to chance constrained programs","publication_year":2014,"publication_date":"2014-06-01","ids":{"openalex":"https://openalex.org/W1997543272","doi":"https://doi.org/10.1109/acc.2014.6859159","mag":"1997543272"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2014.6859159","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2014.6859159","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 American Control Conference","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/A5088958348","display_name":"Zinan Zhao","orcid":"https://orcid.org/0000-0002-3101-4574"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zinan Zhao","raw_affiliation_strings":["University of Florida, Gainesville, FL, US","[Dept. of Mech. & Aerosp. Eng., Univ. of Florida, Gainesville, FL, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florida, Gainesville, FL, US","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"[Dept. of Mech. & Aerosp. Eng., Univ. of Florida, Gainesville, FL, USA]","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073597636","display_name":"Mrinal Kumar","orcid":"https://orcid.org/0000-0001-9747-9449"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mrinal Kumar","raw_affiliation_strings":["University of Florida, Gainesville, FL, US","[Dept. of Mech. & Aerosp. Eng., Univ. of Florida, Gainesville, FL, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florida, Gainesville, FL, US","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"[Dept. of Mech. & Aerosp. Eng., Univ. of Florida, Gainesville, FL, USA]","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5912,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.74646479,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9988999962806702,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9955999851226807,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9894000291824341,"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/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.6883268356323242},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6376380920410156},{"id":"https://openalex.org/keywords/bernstein-polynomial","display_name":"Bernstein polynomial","score":0.6108505129814148},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6088570952415466},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.573805034160614},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5449082851409912},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49141085147857666},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4393784999847412},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43901747465133667},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.41767922043800354},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.25848114490509033},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15246552228927612}],"concepts":[{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.6883268356323242},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6376380920410156},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.6108505129814148},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6088570952415466},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.573805034160614},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5449082851409912},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49141085147857666},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4393784999847412},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43901747465133667},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.41767922043800354},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.25848114490509033},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15246552228927612},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2014.6859159","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2014.6859159","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2014 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W73692560","https://openalex.org/W105528418","https://openalex.org/W315644267","https://openalex.org/W1516919007","https://openalex.org/W2028147833","https://openalex.org/W2056760934","https://openalex.org/W2057341677","https://openalex.org/W2099506495","https://openalex.org/W2117781171","https://openalex.org/W2132670515","https://openalex.org/W2136698135","https://openalex.org/W2136796925","https://openalex.org/W2138309709","https://openalex.org/W2143514150","https://openalex.org/W2164499670","https://openalex.org/W2167412190","https://openalex.org/W2798344481","https://openalex.org/W4255975151","https://openalex.org/W6631105899"],"related_works":["https://openalex.org/W2151689585","https://openalex.org/W2380816257","https://openalex.org/W3087071515","https://openalex.org/W4283726152","https://openalex.org/W3093571331","https://openalex.org/W1525770572","https://openalex.org/W1485888979","https://openalex.org/W3172507773","https://openalex.org/W2806680938","https://openalex.org/W4302285290"],"abstract_inverted_index":{"This":[0,39],"paper":[1],"presents":[2],"an":[3],"extension":[4],"of":[5,34,59,68,81],"convex":[6,26],"Bernstein":[7,18,60],"approximations":[8,61],"to":[9],"non-affine":[10,46],"and":[11],"dependent":[12,50],"chance":[13],"constrained":[14],"optimization":[15],"problems.":[16],"The":[17],"approximation":[19],"technique":[20],"transcribes":[21],"probabilistic":[22,47],"constraints":[23,48],"into":[24],"conservative":[25],"deterministic":[27],"constraints,":[28],"relying":[29],"heavily":[30],"upon":[31],"the":[32,56,65,88],"evaluation":[33],"exponential":[35],"moment":[36],"generating":[37],"functions.":[38],"is":[40,62],"a":[41,79],"computationally":[42],"burdensome":[43],"task":[44],"for":[45,75,87],"involving":[49],"random":[51],"variables.":[52],"In":[53],"this":[54],"paper,":[55],"theoretical":[57],"framework":[58],"combined":[63,89],"with":[64,94],"practical":[66],"benefits":[67],"Markov":[69],"chain":[70],"Monte":[71],"Carlo":[72],"(MCMC)":[73],"integration":[74],"its":[76],"use":[77],"in":[78],"range":[80],"high":[82],"dimensional":[83],"applications.":[84],"Numerical":[85],"results":[86],"Bernstein/MCMC":[90],"approach":[91],"are":[92],"compared":[93],"scenario":[95],"approximations.":[96]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
