arXiv subjects

Yongyu Fu

Publications and source records attributed to Yongyu Fu.

2 recordsLinked to original sources

arXiv2026

A reflected forward-backward splitting algorithmic framework

In this paper, we propose a reflected forward-backward splitting algorithic framework for finding a zero of the sum of finitely many monotone op-erators, including maximally monotone operators, cocoercive operators, and monotone and Lipschitz continuous operators. We provide a unified convergence analysis under mild conditions, eliminating the need to analyze the convergence of each algorithm individually. The heuristic strategies for matrix selections are proposed through a numerical experiment, based on which a new algorithm is derived. A further numerical experiment on the regularized saddle-point problem is then presented to demonstrate the effectiveness of the proposed algorithm.

math.OC↗

arXiv2025

Frugal forward-backward splitting methods with deviations

The deviation vectors provide additional degrees of freedom and effectively enhance the flexibility of algorithms. In the literature, the iterative schemes with deviations are constructed and their convergence analyses are performed on an inefficient, algorithm-by-algorithm basis. In this paper, we address these by providing a general framework of frugal forward-backward splitting methods with deviations for finding zeros in the sum of a finite number of maximally monotone operators and cocoercive operators. Our framework encompasses the Douglas--Rachford splitting method with deviations. A unified weak convergence analysis is made under mild conditions. Numerical experiments on Markowitz portfolio optimization problem are given to demonstrate the effectiveness of deviations.

math.OC↗