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In this paper, we propose two new self-adaptive relaxed CQ algorithms to solve the split feasibility problem with multiple output sets, which involve the computation of projections onto half-spaces instead of the computation onto the closed convex sets. Our proposed algorithms with selection technique reduce the computation of projections. And then, as a generalization, we construct two new algorithms to solve the variational inequalities over the solution set of split feasibility problem with multiple output sets. More importantly, strong convergence of all proposed algorithms is proved under suitable conditions. Finally, we conduct numerical experiments to show the efficiency and accuracy of our algorithms compared to some existing results. [ABSTRACT FROM AUTHOR]

In this paper, a general splitting method with alternated inertia and its relaxed version are proposed for solving the split equality problem in Hilbert spaces. The proposed methods combine both the relaxation and alternated inertial techniques to speed up the rate of convergence. Furthermore, the methods employ a simple self-adaptive stepsize, which does not require any prior information about the operator norm. Four options of inertial parameters and relaxation parameters are discussed. The weak convergence of the proposed algorithms is analyzed under mild conditions. Finally, two numerical experiments and an application in signal recovery problem are provided to demonstrate the advantages of the proposed algorithms compared to a recent related one. [ABSTRACT FROM AUTHOR]

In this paper, four modified versions of relaxed CQ algorithms are proposed for solving the split feasibility problems (SFP) in infinite-dimensional real Hilbert spaces. The methods are based on replacing the projection to the half-space with that to the intersection of two half-spaces. The convergence speed is accelerated as the algorithms make use of the previous half-spaces. The stepsize is determined dynamically without requiring any prior information about the operator norm. Furthermore, the proposed algorithms are proven to converge strongly to the minimum-norm solution of the SFP. As an application, we apply our results to signal recovery problems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iterative algorithm for solving the multiple-sets split feasibility problem (MSSFP for short) and the split equality fixed point problem (SEFPP for short) with firmly quasi-nonexpansive operators or nonexpansive operators in real Hilbert spaces. Under mild conditions, we prove strong convergence theorems for the algorithm by using the projection method and the properties of projection operators. The result improves and extends the corresponding ones announced by some others in the earlier and recent literature. [ABSTRACT FROM AUTHOR]