Mathematical modelling of the refractive index reconstruction through global optimization

Gleb Beliakov, Stephen Buckley

    Research output: Contribution to journalArticle


    We examine a mathematical model of non-destructive testing of planar waveguides, based on numerical solution of a nonlinear integral equation. Such problem is ill-posed, and the method of Tikhonov regularization is applied. To minimize Tikhonov functional, and find the parameters of the waveguide, we use two new optimization methods: the cutting angle method of global optimization, and the discrete gradient method of nonsmooth local optimization. We examine how the noise in the experimental data influences the solution, and how the regularization parameter has to be chosen. We show that even with significant noise in the data, the numerical solution is of high accuracy, and the method can be used to process real experimental data..
    Original languageEnglish
    Pages (from-to)389-403
    Number of pages15
    JournalInternational Journal of Pure and Applied Mathematics
    Issue number3
    Publication statusPublished - 2005

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