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Connecting optimization with spectral analysis of tri-diagonal matrices

Abstract : We show that the global minimum (resp. maximum) of a continuous function on a compact set can be approximated from above (resp. from below) by computing the smallest (rest. largest) eigenvalue of a hierarchy of (r × r) tri-diagonal univariate moment matrices of increasing size. Equivalently it reduces to computing the smallest (resp. largest) root of a certain univariate degree-r orthonormal polynomial. This provides a strong connection between the fields of optimization, orthogonal polynomials, numerical analysis and linear algebra, via asymptotic spectral analysis of tri-diagonal symmetric matrices.
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https://hal.laas.fr/hal-02190818
Contributor : Jean Bernard Lasserre <>
Submitted on : Thursday, March 12, 2020 - 1:39:31 PM
Last modification on : Thursday, June 10, 2021 - 3:06:38 AM

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Jean Lasserre. Connecting optimization with spectral analysis of tri-diagonal matrices. Mathematical Programming, Series A, Springer, 2020, ⟨10.1007/s10107-020-01549-3⟩. ⟨hal-02190818v4⟩

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