Full Text: PDF
DOI: 10.23952/jnfa.2025.32
Received June 24, 2025; Accepted September 9, 2025; Published October 23, 2025
Abstract. The split feasibility problem has significant applications in various fields such as medical image reconstruction, signal processing, radiation therapy, and signal recovery. With the widespread adoption of multimodal data and large-scale complex systems, efficiently solving mixed split feasibility problems which involve multiple operator constraints and linear equality conditions is now under the spotlight of research in optimization theory. In this paper, we propose two new accelerated iterative algorithms for MSFP: one accelerates the iterative process through multi-step inertial terms and proves weak convergence in Hilbert spaces; the other one further incorporates the viscosity approximation method to achieve strong convergence. We prove that our algorithm converges strongly under suitable conditions. Finally, numerical results illustrate the performances of our algorithms.
How to Cite this Article:
J. Gong, J. Zhan, J. Wen, Y. Wang, P. Duan, Multi-step inertial accelerated algorithms for solving mixed split feasibility problems, J. Nonlinear Funct. Anal. 2025 (2025) 32.