Outer perturbations of a projection method and two approximation methods for the split equality problem

A new relaxed projection and its applications

“…Combettes [30] compared the outer approximation method with Halpern method (also called the anchor point method) and Dykstra's algorithm, and showed that the outer approximation method has the best numerical behavior. Recently, the authors [31] combined Inner Loop with projection methods to get an outer approximation method for the split equality problems, and futhermore compared it with the relaxed projection method. It concluded that the outer approximation method needs less CPU time.…”

“…Next we show that ω w (x k ) ⊆ C. From (5.12), it follows that lim k→∞ Using Lemma 2.2, we have By using Fukushima's idea, Moudafi [35] introduced a relaxed projection method for the SEP. Recently, many authors further improved Moudafi's method by selecting the stepsizes such that the implementation of the method does not need any priori information about the operator norms [12,31].…”

A new projection method with a dynamic stepsize for the split equality problem

“…Most of current methods for investigating solutions of the SEP (1.1) are projection-based methods. We refer to [1,5,6,7,8,9,10,11,12,13] for the convergence analysis of various projection methods. The first efficient method for the SEP is the alternating CQ algorithm proposed by Moudafi and Al-Shemas [14] as follows:…”