Reconstruction of support of a measure from its moments

    Research output: Contribution to journalConference article

    1 Citation (Scopus)

    Abstract

    In this paper, we address the problem of reconstruction of support of a positive finite Borel measure from its moments. More precisely, given a finite subset of the moments of a measure, we develop a semidefinite program for approximating the support of measure using level sets of polynomials. To solve this problem, a sequence of convex relaxations is provided, whose optimal solution is shown to converge to the support of measure of interest. Moreover, the provided approach is modified to improve the results for uniform measures. Numerical examples are presented to illustrate the performance of the proposed approach.

    Original languageEnglish (US)
    Article number7039677
    Pages (from-to)1911-1916
    Number of pages6
    JournalProceedings of the IEEE Conference on Decision and Control
    Volume2015-February
    Issue numberFebruary
    DOIs
    StatePublished - Jan 1 2014
    Event2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States
    Duration: Dec 15 2014Dec 17 2014

    Fingerprint

    Polynomials
    Moment
    Convex Relaxation
    Semidefinite Program
    Borel Measure
    Level Set
    Optimal Solution
    Converge
    Numerical Examples
    Polynomial
    Subset

    All Science Journal Classification (ASJC) codes

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

    Cite this

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    title = "Reconstruction of support of a measure from its moments",
    abstract = "In this paper, we address the problem of reconstruction of support of a positive finite Borel measure from its moments. More precisely, given a finite subset of the moments of a measure, we develop a semidefinite program for approximating the support of measure using level sets of polynomials. To solve this problem, a sequence of convex relaxations is provided, whose optimal solution is shown to converge to the support of measure of interest. Moreover, the provided approach is modified to improve the results for uniform measures. Numerical examples are presented to illustrate the performance of the proposed approach.",
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    journal = "Proceedings of the IEEE Conference on Decision and Control",
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    Reconstruction of support of a measure from its moments. / Jasour, A. M.; Lagoa, Constantino Manuel.

    In: Proceedings of the IEEE Conference on Decision and Control, Vol. 2015-February, No. February, 7039677, 01.01.2014, p. 1911-1916.

    Research output: Contribution to journalConference article

    TY - JOUR

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    AU - Lagoa, Constantino Manuel

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    N2 - In this paper, we address the problem of reconstruction of support of a positive finite Borel measure from its moments. More precisely, given a finite subset of the moments of a measure, we develop a semidefinite program for approximating the support of measure using level sets of polynomials. To solve this problem, a sequence of convex relaxations is provided, whose optimal solution is shown to converge to the support of measure of interest. Moreover, the provided approach is modified to improve the results for uniform measures. Numerical examples are presented to illustrate the performance of the proposed approach.

    AB - In this paper, we address the problem of reconstruction of support of a positive finite Borel measure from its moments. More precisely, given a finite subset of the moments of a measure, we develop a semidefinite program for approximating the support of measure using level sets of polynomials. To solve this problem, a sequence of convex relaxations is provided, whose optimal solution is shown to converge to the support of measure of interest. Moreover, the provided approach is modified to improve the results for uniform measures. Numerical examples are presented to illustrate the performance of the proposed approach.

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