The Strongly Convergent Relaxed Alternating CQ Algorithms for the Split Equality Problem in Hilbert Spaces. (11th June 2021) - Gao, Fugen; Liu, Xiaoxiao
Abstract: Recently, Moudafi introduced the split equality problem (SEP): find x ∈ C, y ∈ Q such that Ax = By . In this paper, we show that finding a solution of the SEP is equivalent to finding a solution of a coupled fixed-point equation which is an extension of the coupled equation proposed by Yu and Wang. Based on this coupled fixed-point equation, we propose two new relaxed alternating algorithms for the SEP, and we prove that the first relaxed algorithm is weakly convergent and the second is strongly convergent.