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Gradient algorithms for quadratic optimization with fast convergence rates

Pronzato, Luc and Zhigljavsky, Anatoly Alexandrovich 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: 04 Jun 2017 03:00

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