CQ-algorithms for the related problems of split equality problem in Hilbert spaces - Cao, Yu; Peng, Yishuo; Chen, Yasong; Shi, Luoyi (Journal of optimization theory and applications, 2026)
In this paper, we propose four novel CQ-algorithms to solve the split equality problem (SEP) in Hilbert spaces. These algorithms incorporate advanced techniques such as adaptive step sizes, alternate inertia, and dual projections, ensuring weak convergence under mild conditions. Additionally, we extend the algorithms to address the multiple-set split equality problem (MSSEP) by introducing four new iterative methods, which also exhibit weak convergence. To validate the efficiency and superiority of our algorithms, we conduct numerical experiments on signal recovery problems. The results demonstrate that our algorithms outperform existing methods in terms of computational speed and accuracy. Key advantages of our approach include: adaptive step sizes that eliminate the need for prior knowledge of operator norms, alternated inertia to accelerate convergence while maintaining Fejer monotonicity, projections onto the intersection of half-spaces, which simplify computations and enhance efficiency. Our work provides a robust framework for solving SEP and MSSEP, with significant potential for applications in optimization, signal processing, and beyond.