Modeling probability densities with sums of exponentials via polynomial approximation

Bogdan Dumitrescu, Bogdan C. Şicleru, Florin Avram

    Tutkimustuotos: ArtikkeliScientificvertaisarvioitu

    6 Sitaatiot (Scopus)

    Abstrakti

    Abstract We propose a method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on shape-constrained optimization with exponential functions. Each function is lower and upper bounded on sub-intervals by low-degree polynomials. Thus, the constraints can be approximated with polynomial inequalities that can be implemented with linear matrix inequalities. Convexity is preserved, but the problem has now a finite number of constraints. We show how to take advantage of the properties of the exponential function in order to build quickly accurate approximations. The problem used for illustration is the least-squares fitting of a positive sum of exponentials to an empirical probability density function. When the exponents are given, the problem is convex, but we also give a procedure for optimizing the exponents. Several examples show that the method is flexible, accurate and gives better results than other methods for the investigated problems.

    AlkuperäiskieliEnglanti
    Sivut513–525
    JulkaisuJournal of Computational and Applied Mathematics
    Vuosikerta292
    Varhainen verkossa julkaisun päivämäärä30 heinäk. 2015
    DOI - pysyväislinkit
    TilaJulkaistu - 2016
    OKM-julkaisutyyppiA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

    Julkaisufoorumi-taso

    • Jufo-taso 2

    !!ASJC Scopus subject areas

    • Computational Mathematics
    • Applied Mathematics

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