<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper deals with subsampled spectral gradient methods for minimizing finite sums. 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 provided that 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 the variable sample nature of this procedure.</p></abstract>

This paper deals with subsampled spectral gradient methods for minimizing finite sums. 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 provided that 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 the variable sample nature of this procedure.

Subsampled Nonmonotone Spectral Gradient Methods

Department of Mathematics and Informatics, Faculty of Sciences

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Subsampled Nonmonotone Spectral Gradient Methods"}

This paper deals with subsampled spectral gradient methods for minimizing finite sums. Subsample function and gradient approximations are employed in order to...

Subsampled Nonmonotone Spectral Gradient Methods

Published Online: Feb 01, 2020

Page range: 19 - 34

Received: Oct 12, 2018

Accepted: Nov 13, 2019

DOI: https://doi.org/10.2478/caim-2020-0002

Keywords
spectral gradient methods, subsampling strategies, global convergence, nonmonotone line search

© 2020 Stefania Bellavia et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Subsampled Nonmonotone Spectral Gradient Methods

Published Online: Feb 01, 2020

Page range: 19 - 34

Received: Oct 12, 2018

Accepted: Nov 13, 2019

DOI: https://doi.org/10.2478/caim-2020-0002

Keywordsspectral gradient methods, subsampling strategies, global convergence, nonmonotone line search

© 2020 Stefania Bellavia et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
spectral gradient methods, subsampling strategies, global convergence, nonmonotone line search