Modified Relaxed CQ Iterative Algorithms for the Split Feasibility Problem
نویسندگان
چکیده
منابع مشابه
Iterative algorithms based on the hybrid steepest descent method for the split feasibility problem
In this paper, we introduce two iterative algorithms based on the hybrid steepest descent method for solving the split feasibility problem. We establish results on the strong convergence of the sequences generated by the proposed algorithms to a solution of the split feasibility problem, which is a solution of a certain variational inequality. In particular, the minimum norm solution of the spl...
متن کاملA 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 ∥
متن کاملApproximating Curve and Strong Convergence of the CQ Algorithm for the Split Feasibility Problem
Using the idea of Tikhonov’s regularization, we present properties of the approximating curve for the split feasibility problem SFP and obtain the minimum-norm solution of SFP as the strong limit of the approximating curve. It is known that in the infinite-dimensional setting, Byrne’s CQ algorithm Byrne, 2002 has only weak convergence. We introduce a modification of Byrne’s CQ algorithm in such...
متن کاملA Modified Algorithm for Solving the Split Feasibility Problem
In this paper a modified algorithm for solving the split feasibility problem (SFP) is presented. This algorithm uses the generalized Armijo line search in computing predictor step size and gives a correction step rule in the iterative process, which makes an accelerated convergence to the solution of SFP. Meanwhile, it needs not to compute the matrix inverses and the large eigenvalue of the mat...
متن کاملNew generalized variable stepsizes of the CQ algorithm for solving the split feasibility problem
Variable stepsize methods are effective for various modified CQ algorithms to solve the split feasibility problem (SFP). The purpose of this paper is first to introduce two new simpler variable stepsizes of the CQ algorithm. Then two new generalized variable stepsizes which can cover the former ones are also proposed in real Hilbert spaces. And then, two more general KM (Krasnosel'skii-Mann)-CQ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2019
ISSN: 2227-7390
DOI: 10.3390/math7020119