This paper deals with subsampled spectral gradient methods for minimizing finite sum. Subsample function and gradient approximations are employed in order to reduce the overall computational cost of the classical spectral gradient methods. The global convergence is enforced by a nonmonotone line search procedure. Global convergence is proved when functions and gradients are approximated with increasing accuracy. R-linear convergence and worst-case iteration complexity is investigated in case of strongly convex objective function. Numerical results on well known binary classification problems are given to show the effectiveness of this framework and analyze the effect of different spectral coefficient approximations arising from variable sample nature of this procedure.
Subsampled Nonmonotone Spectral Gradient Methods / STEFANIA BELLAVIA, Nataša Krklec Jerinkić, Greta Malaspina. - In: COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS. - ISSN 2038-0909. - STAMPA. - 11:(2020), pp. 19-34. [10.2478/caim-2020-0002]
Subsampled Nonmonotone Spectral Gradient Methods
STEFANIA BELLAVIA
;Greta Malaspina
2020
Abstract
This paper deals with subsampled spectral gradient methods for minimizing finite sum. Subsample function and gradient approximations are employed in order to reduce the overall computational cost of the classical spectral gradient methods. The global convergence is enforced by a nonmonotone line search procedure. Global convergence is proved when functions and gradients are approximated with increasing accuracy. R-linear convergence and worst-case iteration complexity is investigated in case of strongly convex objective function. Numerical results on well known binary classification problems are given to show the effectiveness of this framework and analyze the effect of different spectral coefficient approximations arising from variable sample nature of this procedure.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.