CQ-Like Algorithm for Nonconvex Split Feasibility Problem with Multiple Output Sets

With the development of science and technology, many practical problems can be transformed into nonconvex problems. As far as we know, current research on nonconvex split feasibility problems, especially on nonconvex split feasibility problems with multiple output sets, remains relatively limited. To address this need, we propose a CQ-like algorithm to solve them. This new algorithm extends the applicability of the CQ algorithm from two sets to multiple sets, and optimizes the step size to reduce the number of iterations. The convergence and convergence rates of the proposed algorithm for semialgebraic sets are proven by using the Kurdyka–Łojasiewicz inequality. Additionally, we apply the algorithm to diverse signal and image recovery problems, and compare its effectiveness with other existing algorithms. Numerical experiments reveal that the proposed algorithm demonstrates superior efficiency and practicality.