A Double Inertial Forward-Backward Splitting Algorithm With Applications to Regression and Classification Problems
İrfan Işik, Ibrahim Karahan, Okan Erkaymaz
TL;DR
The paper tackles monotone inclusion problems of the form $0\in Az+Bz$ in real Hilbert spaces, where $A$ is $\alpha$-co-coercive and $B$ is maximal monotone. It introduces a novel double inertial forward-backward splitting algorithm (Algorithm 1*) and proves its weak convergence to a zero of $A+B$ under standard assumptions. The method is cast as a fixed-point iteration with a $\kappa$-averaged operator and is supported by numerical experiments in regression and classification, showing competitive or superior performance against established algorithms. The work contributes a theoretically sound acceleration technique for variational problems with practical implications for regression and data classification, demonstrated via synthetic data and an Iris dataset experiment. Future work includes optimizing convergence rates and extending applicability to broader problem classes.
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.