A Double Inertial Forward-Backward Splitting Algorithm With Applications to Regression and Classification Problems

TL;DR

This paper introduces an enhanced inertial forward-backward splitting algorithm with two inertial parameters, demonstrating weak convergence and superior performance in regression and classification tasks through extensive experiments.

Contribution

It proposes a novel double inertial forward-backward splitting algorithm with proven weak convergence and improved empirical performance over existing methods.

Findings

Algorithm shows weak convergence under standard assumptions.

Experimental results outperform existing algorithms in regression tasks.

Superior results in classification problems compared to benchmarks.

Abstract

This paper presents an improved forward-backward splitting algorithm with two inertial parameters. It aims to find a point in the real Hilbert space at which the sum of a co-coercive operator and a maximal monotone operator vanishes. Under standard assumptions, our proposed algorithm demonstrates weak convergence. We present numerous experimental results to demonstrate the behavior of the developed algorithm by comparing it with existing algorithms in the literature for regression and data classification problems. Furthermore, these implementations suggest our proposed algorithm yields superior outcomes when benchmarked against other relevant algorithms in existing literature.