Hybrid simultaneous algorithms for the split equality problem with applications

Abstract

The split equality problem has board applications in many areas of applied mathematics. Many researchers studied this problem and proposed various algorithms to solve it. From the literature we know that most algorithms for the split equality problems came from the idea of the projected Landweber algorithm proposed by Byrne and Moudafi (Working paper UAG, 2013), and few algorithms came from the idea of the alternating CQ-algorithm given by Moudafi (Nonlinear Anal. 79:117-121, 2013). Hence, it is important and necessary to give new algorithms from the idea of the alternating CQ-algorithm. In this paper, we first present a hybrid projected Landweber algorithm to study the split equality problem. Next, we propose a hybrid alternating CQ-algorithm to study the split equality problem. As applications, we consider the split feasibility problem and linear inverse problem. Finally, we give numerical results for the split feasibility problem to demonstrate the efficiency of the proposed algorithms. MSC: 49J53; 49M37; 90C25

Simultaneous and semi-alternating projection algorithms for solving split equality problems

“…Employing arguments which are similar to those used in Remark 3.4 , comparing ( 69 ) and (2.48) in [ 15 ], we conclude that Algorithm 3.2 (I) has a better contraction property than the hybrid alternating CQ-algorithm in [ 15 ].…”

“…Inspired by Algorithm 2.2 in [ 15 ] and based on Algorithm 3.1 , we present two semi-alternating projection algorithms, whose name comes from an alternating technique taken in the first step.…”

“…Recently, Chuang and Du [ 15 ] proposed the following projection algorithm (which is called the hybrid projected Landweber algorithm).…”

“…Chuang and Du [ 15 ] proved the convergence of Algorithm 1.2 and also presented the convergence property of Algorithm 1.2 as follows: where .…”

Latent Infectious Capacities of Dengue Fever: Mathematical Modeling and Eco-Friendly Prevention Strategy

“…Later, Yao et al [28,29] extended the regularization method to approach the solution of SFP (4). Some works [30][31][32][33][34][35][36] also developed generalized fixed point algorithms which can be applied to approach the solution of SFP. In particular, the iterative scheme, expressed as the following Equation (8), proposed by Hong and Huang [32], has shown that it can efficiently approach the solution of SFP: Theorem 3.…”