{"id":"https://openalex.org/W2058232556","doi":"https://doi.org/10.1109/cdc.2011.6161308","title":"Randomized min-max optimization: The exact risk of multiple cost levels","display_name":"Randomized min-max optimization: The exact risk of multiple cost levels","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2058232556","doi":"https://doi.org/10.1109/cdc.2011.6161308","mag":"2058232556"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2011.6161308","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6161308","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European 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":null,"display_name":"Algo Car`e","orcid":null},"institutions":[{"id":"https://openalex.org/I79940851","display_name":"University of Brescia","ror":"https://ror.org/02q2d2610","country_code":"IT","type":"education","lineage":["https://openalex.org/I79940851"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Algo Car`e","raw_affiliation_strings":["Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Brescia, via Branze 38, 25123, Italia"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Brescia, via Branze 38, 25123, Italia","institution_ids":["https://openalex.org/I79940851"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080248970","display_name":"Simone Garatti","orcid":"https://orcid.org/0000-0002-5451-6892"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Simone Garatti","raw_affiliation_strings":["Dipartimento di Elettronica e In-formazione, Politecnico di Milano, Milano, Italia"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Elettronica e In-formazione, Politecnico di Milano, Milano, Italia","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068752903","display_name":"Marco C. Campi","orcid":"https://orcid.org/0000-0002-5209-3312"},"institutions":[{"id":"https://openalex.org/I79940851","display_name":"University of Brescia","ror":"https://ror.org/02q2d2610","country_code":"IT","type":"education","lineage":["https://openalex.org/I79940851"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco C. Campi","raw_affiliation_strings":["Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Brescia, Brescia, Italia"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria dell'Informazione, Universit\u00e0 di Brescia, Brescia, Italia","institution_ids":["https://openalex.org/I79940851"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I79940851"],"apc_list":null,"apc_paid":null,"fwci":0.9831,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.81304576,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"30","issue":null,"first_page":"7794","last_page":"7799"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9993000030517578,"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":0.9993000030517578,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5852599740028381},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5842039585113525},{"id":"https://openalex.org/keywords/risk-measure","display_name":"Risk measure","score":0.5353143215179443},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.5300842523574829},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.5138395428657532},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.5054464340209961},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4839092195034027},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.4807174503803253},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.4573078453540802},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4442311227321625},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33184361457824707},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3245888650417328},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2566130757331848}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5852599740028381},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5842039585113525},{"id":"https://openalex.org/C2781472820","wikidata":"https://www.wikidata.org/wiki/Q2154759","display_name":"Risk measure","level":3,"score":0.5353143215179443},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.5300842523574829},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.5138395428657532},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.5054464340209961},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4839092195034027},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4807174503803253},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.4573078453540802},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4442311227321625},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33184361457824707},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3245888650417328},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2566130757331848},{"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/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","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/C2780821815","wikidata":"https://www.wikidata.org/wiki/Q5340806","display_name":"Portfolio","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2011.6161308","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2011.6161308","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Conference on Decision and Control and European 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":34,"referenced_works":["https://openalex.org/W110885661","https://openalex.org/W1486549947","https://openalex.org/W1541527977","https://openalex.org/W1579369571","https://openalex.org/W1976466849","https://openalex.org/W1999732675","https://openalex.org/W2058232556","https://openalex.org/W2076179404","https://openalex.org/W2078844657","https://openalex.org/W2088298783","https://openalex.org/W2103012681","https://openalex.org/W2104371886","https://openalex.org/W2106154407","https://openalex.org/W2117781171","https://openalex.org/W2125107769","https://openalex.org/W2150664153","https://openalex.org/W2164499670","https://openalex.org/W2167412190","https://openalex.org/W2170344528","https://openalex.org/W2296319761","https://openalex.org/W2313727555","https://openalex.org/W2592903912","https://openalex.org/W3212877690","https://openalex.org/W4233413206","https://openalex.org/W4236670843","https://openalex.org/W4241962560","https://openalex.org/W4245714805","https://openalex.org/W4247165901","https://openalex.org/W4248266779","https://openalex.org/W4250589301","https://openalex.org/W4250913065","https://openalex.org/W4294968333","https://openalex.org/W6685056065","https://openalex.org/W6734267016"],"related_works":["https://openalex.org/W2016318053","https://openalex.org/W1985367615","https://openalex.org/W3047490334","https://openalex.org/W2978562669","https://openalex.org/W1483187394","https://openalex.org/W3124205382","https://openalex.org/W3123325486","https://openalex.org/W3152252745","https://openalex.org/W2261871379","https://openalex.org/W2105067139"],"abstract_inverted_index":{"In":[0],"this":[1,49,97],"paper,":[2],"we":[3],"present":[4],"a":[5,34,75,86,104,138],"theoretical":[6,93],"result":[7,94,140],"that":[8,80,100],"applies":[9],"to":[10,61,66,74,133],"convex":[11],"optimization":[12],"problems":[13],"in":[14,51,96],"the":[15,24,29,40,45,54,63,67,71,78,81,101,118,122,130,134,142,145],"presence":[16],"of":[17,37,39,53,117,121,144],"an":[18,112],"uncertain":[19,41,123],"stochastic":[20,42,124],"parameter.":[21,125],"We":[22],"consider":[23],"min-max":[25,30,146],"sample-based":[26,147],"solution,":[27],"i.e.":[28],"solution":[31,50],"computed":[32],"over":[33],"finite":[35],"sample":[36],"instances":[38],"parameter,":[43],"and":[44,136],"costs":[46],"incurred":[47],"by":[48],"correspondence":[52],"sampled":[55],"parameter":[56],"instances.":[57],"Our":[58],"goal":[59],"is":[60,77,83,90,99,110],"evaluate":[62],"risks":[64,102,131],"associated":[65,73,132],"various":[68],"costs,":[69,135],"where":[70],"risk":[72],"cost":[76,82],"probability":[79,108,119],"exceeded":[84],"when":[85],"new":[87],"uncertainty":[88],"instance":[89],"seen.":[91],"The":[92],"proven":[95],"paper":[98],"form":[103],"random":[105],"vector":[106],"whose":[107],"distribution":[109],"always":[111],"ordered":[113],"Dirichlet":[114],"distribution,":[115],"irrespective":[116],"measure":[120],"This":[126],"evaluation":[127],"characterizes":[128],"completely":[129],"represents":[137],"full-fledged":[139],"on":[141],"reliability":[143],"solution.":[148]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}