Moments, Positive Polynomials And Their Applications

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Moments, Positive Polynomials And Their Applications
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  1. Beskrivelse

    colour illustrations

    Udgivelsesdato:
    02-10-2009
    Leveringstid:
    5-9 hverdage
    Rating:
    (0)
  2. Yderligere info
    Udgivelsesdato:
    02-10-2009
    Sprog:
    Engelsk
    ISBN13:
    9781911299738
    Sidetal:
    384
    Vægt:
    514
    Højde:
    20
    Bredde:
    152
    Længde:
    229
    Nummer i serien:
    1
    Mærkat:
    Bog, paperback
    Format:
    Paperback
    • Bibliotekernes beskrivelse

      Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP). This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones, standard duality in convex optimization nicely expresses the duality between moments and positive polynomials. In the second part, the methodology is particularized and described in detail for various applications, including global optimization, probability, optimal control, mathematical finance, multivariate integration, etc., and examples are provided for each particular application.

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