An asymptotically optimal gradient algorithm for quadratic optimization with low computational cost

Zhigljavsky, Anatoly ORCID: https://orcid.org/0000-0003-0630-8279, Pronzato, Luc and Bukina, Elena 2013. An asymptotically optimal gradient algorithm for quadratic optimization with low computational cost. Optimization Letters 7 (6) , pp. 1047-1059. 10.1007/s11590-012-0491-7

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Abstract

We consider gradient algorithms for minimizing a quadratic function in Rn with large n. We suggest a particular sequence of step-sizes and demonstrate that the resulting gradient algorithm has a convergence rate comparable with that of Conjugate Gradients and other methods based on the use of Krylov spaces. When the matrix is large and sparse, the proposed algorithm can be more efficient than the Conjugate Gradient algorithm in terms of computational cost, as k iterations of the proposed algorithm only require the computation of O(log k) inner products.

Item Type:	Article
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Quadratic optimization, Gradient algorithms, Conjugate gradient, Arcsine distribution, Fibonacci numbers, Estimation of leading eigenvalues
Publisher:	Springer Berlin Heidelberg
ISSN:	1862-4472
Last Modified:	01 Nov 2022 09:55
URI:	https://orca.cardiff.ac.uk/id/eprint/89667

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