Gradient algorithms for quadratic optimization with fast convergence rates

Pronzato, Luc and Zhigljavsky, Anatoly Alexandrovich ORCID: https://orcid.org/0000-0003-0630-8279 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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Abstract

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
URI:	https://orca.cardiff.ac.uk/id/eprint/15200

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