# Subsampled Nonmonotone Spectral Gradient Methods

## TL;DR

This paper introduces subsampled spectral gradient methods with nonmonotone line search for efficient finite-sum minimization, demonstrating convergence and effectiveness through theoretical analysis and numerical experiments on classification tasks.

## Contribution

It proposes a novel subsampled spectral gradient framework with nonmonotone line search, providing convergence guarantees and complexity analysis for large-scale optimization.

## Key findings

- Global convergence proved with increasing approximation accuracy.
- R-linear convergence shown for strongly convex functions.
- Numerical results confirm effectiveness on binary classification problems.

## 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.