We propose a family of gradient algorithms for minimizing a quadratic function f(x) = (Ax; x)=2 ¡ (x; y) in Rd 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 < 1 the space dimension.
Source: Cardiff University
Author: Luc Pronzato | Anatoly Zhigljavsky
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