🤖 AI Summary
This paper addresses the problem of finding zeros of the sum of a co-coercive operator and a maximally monotone operator in real Hilbert spaces—a formulation that unifies various regression and classification tasks. To this end, we propose a novel doubly inertial forward–backward splitting algorithm, the first to incorporate two independent, tunable inertia parameters. Crucially, this design accelerates convergence and enhances numerical stability without incurring additional computational cost. Under standard assumptions of monotonicity and co-coercivity, we establish rigorous weak convergence of the generated iterates. Our theoretical analysis integrates tools from operator splitting, inertial acceleration, and monotone operator theory. Extensive experiments on benchmark regression and classification tasks demonstrate that the proposed method achieves faster convergence and higher accuracy than classical and recent forward–backward-type algorithms, delivering consistent state-of-the-art performance.
📝 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.