Consiglio Nazionale delle Ricerche

Tipo di prodottoArticolo in rivista
TitoloA Randomized Strategy for Probabilistic Solutions of Uncertain Feasibility and Optimization Problems
Anno di pubblicazione2009
Formato
  • Elettronico
  • Cartaceo
Autore/iT. Alamo, R. Tempo, E. F. Camacho
Affiliazioni autoriR. Tempo: CNR-IEIIT T. Alamo: University of Sevilla E.F. Camacho: University of Sevilla
Autori CNR e affiliazioni
  • ROBERTO TEMPO VQR
Lingua/e
  • inglese
AbstractIn 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.
Lingua abstractinglese
Altro abstract-
Lingua altro abstract-
Pagine da2545
Pagine a2559
Pagine totali-
RivistaIEEE transactions on automatic control (Print)
Attiva dal 1963
Editore: Institute of Electrical and Electronics Engineers, - New York, N.Y.
Paese di pubblicazione: Stati Uniti d'America
Lingua: inglese
ISSN: 0018-9286
Titolo chiave: IEEE transactions on automatic control (Print)
Titolo proprio: IEEE transactions on automatic control. (Print)
Titolo abbreviato: IEEE trans. automat. contr. (Print)
Titoli alternativi:
  • Transactions on automatic control (Print)
  • Automatic control (Print)
Numero volume della rivista54/11
Fascicolo della rivista-
DOI10.1109/TAC.2010.2042984
Verificato da refereeSì: Internazionale
Stato della pubblicazione-
Indicizzazione (in banche dati controllate)
  • ISI Web of Science (WOS) (Codice:WOS:000271436600006)
Parole chiaveProbabilistic robustness; randomized algorithms; statistical learning theory; uncertain systems
Link (URL, URI)-
Titolo parallelo-
Data di accettazione-
Note/Altre informazioni-
Strutture CNR
  • IEIIT — Istituto di elettronica e di ingegneria dell'informazione e delle telecomunicazioni
Moduli CNR
    Progetti Europei-
    Allegati
    • A Randomized Strategy for Probabilistic Solutions of Uncertain Feasibility and Optimization Problems

    Dati storici
    I dati storici non sono modificabili, sono stati ereditati da altri sistemi (es. Gestione Istituti, PUMA, ...) e hanno solo valore storico.
    Area disciplinareComputer Science & Engineering
    Area valutazione CIVRIngegneria industriale e informatica
    Rivista ISIIEEE TRANSACTIONS ON AUTOMATIC CONTROL [42592J0]