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Gradient algorithms for quadratic optimization with fast convergence rates

Pronzato, Luc and Zhigljavsky, Anatoly Alexandrovich ORCID: 2011. Gradient algorithms for quadratic optimization with fast convergence rates. Computational Optimization and Applications 50 (3) , pp. 597-617. 10.1007/s10589-010-9319-5

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We propose a family of gradient algorithms for minimizing a quadratic function f(x)=(Ax,x)/2−(x,y) in ℝ d or a Hilbert space, with simple rules for choosing the step-size at each iteration. We show that when the step-sizes are generated by a dynamical system with ergodic distribution having the arcsine density on a subinterval of the spectrum of A, the asymptotic rate of convergence of the algorithm can approach the (tight) bound on the rate of convergence of a conjugate gradient algorithm stopped before d iterations, with d≤∞ the space dimension.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Springer Verlag
ISSN: 0926-6003
Last Modified: 03 May 2023 09:08

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