@prefix prodottidellaricerca: . @prefix istituto: . @prefix prodotto: . istituto:CDS029 prodottidellaricerca:prodotto prodotto:ID20719 . @prefix pubblicazioni: . @prefix unitaDiPersonaleInterno: . unitaDiPersonaleInterno:MATRICOLA20115 pubblicazioni:autoreCNRDi prodotto:ID20719 . @prefix modulo: . modulo:ID2244 prodottidellaricerca:prodotto prodotto:ID20719 . @prefix rdf: . @prefix retescientifica: . prodotto:ID20719 rdf:type retescientifica:ProdottoDellaRicerca , prodotto:TIPO1101 . @prefix rdfs: . prodotto:ID20719 rdfs:label "A Randomized Strategy for Probabilistic Solutions of Uncertain Feasibility and Optimization Problems (Articolo in rivista)"@en . @prefix xsd: . prodotto:ID20719 pubblicazioni:anno "2009-01-01T00:00:00+01:00"^^xsd:gYear ; pubblicazioni:doi "10.1109/TAC.2010.2042984"^^xsd:string . @prefix skos: . prodotto:ID20719 skos:altLabel "
T. Alamo, R. Tempo, E. F. Camacho (2009)
A Randomized Strategy for Probabilistic Solutions of Uncertain Feasibility and Optimization Problems
in IEEE transactions on automatic control (Print)
"^^rdf:HTML ; pubblicazioni:autori "T. Alamo, R. Tempo, E. F. Camacho"^^xsd:string ; pubblicazioni:paginaInizio "2545"^^xsd:string ; pubblicazioni:paginaFine "2559"^^xsd:string ; pubblicazioni:numeroVolume "54/11"^^xsd:string . @prefix ns11: . prodotto:ID20719 pubblicazioni:rivista ns11:ID394449 ; skos:note "ISI Web of Science (WOS)"^^xsd:string ; pubblicazioni:affiliazioni "R. Tempo: CNR-IEIIT\nT. Alamo: University of Sevilla\nE.F. Camacho: University of Sevilla"^^xsd:string ; pubblicazioni:titolo "A Randomized Strategy for Probabilistic Solutions of Uncertain Feasibility and Optimization Problems"^^xsd:string ; prodottidellaricerca:abstract "In this paper, we study two general semi-infinite programming problems by means of a randomized strategy based on statistical learning theory. The sample size results obtained with this approach are generally considered to be very conservative by the control community. The first main contribution of this paper is to demonstrate that this is not necessarily the case. Utilizing as a starting point one-sided results from statistical learning theory, we obtain bounds on the number of required samples that are manageable for \\\"reasonable\\\" values of probabilistic confidence and accuracy. In particular, we show that the number of required samples grows with the accuracy parameter epsilon as 1/epsilon in 1/epsilon, and this is a significant improvement when compared to the existing bounds which depend on 1/epsilon(2) ln 1/epsilon(2). Secondly, we present new results for optimization and feasibility problems involving Boolean expressions consisting of polynomials. In this case, when the accuracy parameter is sufficiently small, an explicit bound that only depends on the number of decision variables, and on the confidence and accuracy parameters is presented. For convex optimization problems, we also prove that the required sample size is inversely proportional to the accuracy for fixed confidence. Thirdly, we propose a randomized algorithm that provides a probabilistic solution circumventing the potential conservatism of the bounds previously derived."@en ; prodottidellaricerca:prodottoDi istituto:CDS029 , modulo:ID2244 ; pubblicazioni:autoreCNR unitaDiPersonaleInterno:MATRICOLA20115 . @prefix parolechiave: . prodotto:ID20719 parolechiave:insiemeDiParoleChiave . ns11:ID394449 pubblicazioni:rivistaDi prodotto:ID20719 . parolechiave:insiemeDiParoleChiaveDi prodotto:ID20719 .