{"id":"https://openalex.org/W2004959978","doi":"https://doi.org/10.1109/cacsd.2010.5612829","title":"Random convex programs part 2","display_name":"Random convex programs part 2","publication_year":2010,"publication_date":"2010-09-01","ids":{"openalex":"https://openalex.org/W2004959978","doi":"https://doi.org/10.1109/cacsd.2010.5612829","mag":"2004959978"},"language":"en","primary_location":{"id":"doi:10.1109/cacsd.2010.5612829","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cacsd.2010.5612829","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Symposium on Computer-Aided Control System Design","raw_type":"proceedings-article"},"type":"conference-paper","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/A5041746196","display_name":"Giuseppe C. Calafiore","orcid":"https://orcid.org/0000-0002-6428-5653"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Giuseppe Carlo Calafiore","raw_affiliation_strings":["Dipartimento di Automatica e Infromatica, Politecnico di Torino, Italy","Dipartimento di Automatica e Informatica - Politecnico di Torino, ITALY#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Automatica e Infromatica, Politecnico di Torino, Italy","institution_ids":["https://openalex.org/I177477856"]},{"raw_affiliation_string":"Dipartimento di Automatica e Informatica - Politecnico di Torino, ITALY#TAB#","institution_ids":["https://openalex.org/I177477856"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041746196"],"corresponding_institution_ids":["https://openalex.org/I177477856"],"apc_list":null,"apc_paid":null,"fwci":1.519,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.82220401,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1546","last_page":"1552"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9995999932289124,"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":0.9995999932289124,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9868000149726868,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7113138437271118},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6924951672554016},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5980579853057861},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4962063431739807},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.49193549156188965},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47956961393356323},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4610196352005005},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4163421392440796},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.41222625970840454}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7113138437271118},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6924951672554016},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5980579853057861},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4962063431739807},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.49193549156188965},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47956961393356323},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4610196352005005},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4163421392440796},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.41222625970840454},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cacsd.2010.5612829","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cacsd.2010.5612829","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Symposium on Computer-Aided Control System Design","raw_type":"proceedings-article"},{"id":"pmh:oai:porto.polito.it:2380899","is_oa":false,"landing_page_url":"http://porto.polito.it/2380899/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402038","display_name":"PORTO Publications Open Repository TOrino (Politecnico di Torino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177477856","host_organization_name":"Politecnico di Torino","host_organization_lineage":["https://openalex.org/I177477856"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:porto.polito.it:2380900","is_oa":false,"landing_page_url":"http://porto.polito.it/2380900/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402038","display_name":"PORTO Publications Open Repository TOrino (Politecnico di Torino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177477856","host_organization_name":"Politecnico di Torino","host_organization_lineage":["https://openalex.org/I177477856"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7900000214576721,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W49747896","https://openalex.org/W66371144","https://openalex.org/W88909337","https://openalex.org/W1546638125","https://openalex.org/W1789652828","https://openalex.org/W1976466849","https://openalex.org/W1987420866","https://openalex.org/W2006093909","https://openalex.org/W2007668370","https://openalex.org/W2010790640","https://openalex.org/W2014838276","https://openalex.org/W2042587503","https://openalex.org/W2073335364","https://openalex.org/W2084575717","https://openalex.org/W2089105401","https://openalex.org/W2096999004","https://openalex.org/W2099506495","https://openalex.org/W2115347893","https://openalex.org/W2117781171","https://openalex.org/W2125107769","https://openalex.org/W2143514150","https://openalex.org/W2148603752","https://openalex.org/W2150664153","https://openalex.org/W2158479468","https://openalex.org/W2167412190","https://openalex.org/W2482620286","https://openalex.org/W2798344481","https://openalex.org/W2908064020","https://openalex.org/W2916123017","https://openalex.org/W4211143138","https://openalex.org/W4362223079","https://openalex.org/W6602052592","https://openalex.org/W6638417329","https://openalex.org/W6651414310"],"related_works":["https://openalex.org/W4388311650","https://openalex.org/W5922282","https://openalex.org/W1974056099","https://openalex.org/W4245343541","https://openalex.org/W2386077341","https://openalex.org/W563589758","https://openalex.org/W62490179","https://openalex.org/W2954004777","https://openalex.org/W2951102138","https://openalex.org/W3153752017"],"abstract_inverted_index":{"In":[0,26,87],"the":[1,18,27,32,36,51,57,74,89,111,120,136,140],"companion":[2],"paper":[3],"we":[4,30],"introduced":[5],"a":[6,45,115],"theory":[7],"for":[8,17,70],"random":[9],"convex":[10],"programs":[11],"(RCPs),":[12],"deriving":[13],"tight":[14],"upper":[15,108],"bounds":[16,67],"probability":[19,58],"of":[20,38,59,92,114,123,139],"optimal":[21,52,90,112,121,127,137],"objective":[22,53,60,91,113,122,138],"and":[23,65,73,78],"constraint":[24,97,128],"violation.":[25],"present":[28],"paper,":[29],"extend":[31],"basic":[33],"setup":[34],"to":[35,49,133],"case":[37],"RCPs":[39],"with":[40,95,101,126],"a-posteriori":[41],"violated":[42],"constraints":[43],"(RCPVs):":[44],"paradigm":[46],"that":[47],"permits":[48],"improve":[50],"value":[54],"while":[55],"maintaining":[56],"violation":[61],"under":[62,83],"control.":[63],"Explicit":[64],"non-asymptotic":[66],"are":[68],"derived":[69],"this":[71],"case,":[72],"relation":[75],"between":[76],"RCPVs":[77,125],"chance-constrained":[79,117,141],"problems":[80],"is":[81],"highlighted,":[82],"no":[84],"feasibility":[85],"assumption.":[86],"particular,":[88],"an":[93,105,124],"RCPV":[94],"generic":[96],"removal":[98,129],"rule":[99,130],"provides,":[100],"arbitrarily":[102],"high":[103],"probability,":[104],"efficiently":[106],"computable":[107],"bound":[109],"on":[110],"corresponding":[116],"problem.":[118,142],"Further,":[119],"can":[131],"approximate":[132],"arbitrary":[134],"level":[135]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
