Accelerated Gradient-CQ Algorithms for Split Feasibility Problems

This work focuses on split feasibility problems in Hilbert spaces. To accelerate the convergent rate of gradient-CQ algorithms, we introduce an inertial term. Additionally, non-monotone stepsizes are employed to adjust the relaxation parameter applied to the original stepsizes, ensuring that these original stepsizes maintain a positive lower bound. Thereby, the efficiency of the algorithms is improved. Moreover, the weak and strong convergence of the proposed algorithms are established through proofs that exhibit a similar symmetry structure and do not require the assumption of Lipschitz continuity for the gradient mappings. Finally, the LASSO problem is presented to illustrate and compare the performance of the algorithms.