Asymptotic behaviour of a family of gradient algorithms in R^d and {H}ilbert spaces.
Luc Pronzato, Henry Wynn and A.A. Zhigljavsky
Mathematical Programming 2005.

Abstract

This paper extends previous work on the study of the behaviour of renormalised gradient algorithms, giving general results which apply in finite dimensions and in Hilbert space. The original result, which is that convergence is to a two-point attractor is studied in more details and for a wider class of algorithms. Use is made of moment theory in the search for suitable Lyaponouv functions to control convergence rates, in the worst and average cases.

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