Modified Projection Algorithms for Solving the Split Equality Problems

Modified Projection Algorithms for Solving the Split Equality Problems

The split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013) proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an additional projection step onto two half-spaces in each iteration. We further propo...

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

In this article, we first introduce two simultaneous projection algorithms for solving the split equality problem by using a new choice of the stepsize, and then propose two semi-alternating projection algorithms. The weak convergence of the proposed algorithms is analyzed under standard conditions. As applications, we extend the results to solve the split feasibility problem. Finally, a numeri...

A Modified Halpern’s Iterative Scheme for Solving Split Feasibility Problems

and Applied Analysis 3 PK is called the metric projection ofH ontoK. It is well known that PK is a nonexpansive mapping ofH onto K and satisfies 〈x − y, PKx − PKy〉 ≥ ∥ PKx − PKy ∥ ∥ 2 , 2.3 for every x, y ∈ H. Moreover, PKx is characterized by the following properties: PKx ∈ K and 〈x − PKx, y − PKx〉 ≤ 0, ∥ ∥x − y∥∥ ≥ ‖x − PKx‖ ∥ ∥y − PKx ∥

On Projection Algorithms for Solving Convex Feasibility Problems

Due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences (most notably, computerized tomography), algorithms for solving convex feasibility problems continue to receive great attention. To unify, generalize, and review some of these algorithms, a very broad and exible framework is investigated. Several crucial new concepts wh...

Modified Halfspace-Relaxation Projection Methods for Solving the Split Feasibility Problem