Uniform sample generation in semialgebraic sets

Fabrizio Dabbene, Didier Henrion, Constantino Lagoa

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    1 Scopus citations

    Abstract

    We propose efficient techniques for generating independent identically distributed uniform random samples inside semialgebraic sets. The proposed algorithm leverages recent results on the approximation of indicator functions by polynomials to develop acceptance/rejection based sample generation algorithms with guaranteed performance in terms of rejection rate (the number of samples that should be generated in order to obtain an accepted sample). Moreover, the acceptance rate is shown to be asymptotically optimal, in the sense that it tends to one (all samples accepted) as the degree of the polynomial approximation increases. The performance of the proposed method is illustrated by a numerical example.

    Original languageEnglish (US)
    Title of host publication53rd IEEE Conference on Decision and Control,CDC 2014
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages5177-5182
    Number of pages6
    EditionFebruary
    ISBN (Electronic)9781479977468
    DOIs
    StatePublished - 2014
    Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
    Duration: Dec 15 2014Dec 17 2014

    Publication series

    NameProceedings of the IEEE Conference on Decision and Control
    NumberFebruary
    Volume2015-February
    ISSN (Print)0743-1546
    ISSN (Electronic)2576-2370

    Other

    Other2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014
    Country/TerritoryUnited States
    CityLos Angeles
    Period12/15/1412/17/14

    All Science Journal Classification (ASJC) codes

    • Control and Systems Engineering
    • Modeling and Simulation
    • Control and Optimization

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