Regularized Methods for the Split Feasibility Problem

Yonghong Yao,Wu Jigang,Yeong-Cheng Liou

doi:10.1155/2012/140679

Yonghong Yao, Wu Jigang + Show 1 more

Open Access

https://doi.org/10.1155/2012/140679

Copy DOI

Abstract

Many applied problems such as image reconstructions and signal processing can be formulated as the split feasibility problem (SFP). Some algorithms have been introduced in the literature for solving the (SFP). In this paper, we will continue to consider the convergence analysis of the regularized methods for the (SFP). Two regularized methods are presented in the present paper. Under some different control conditions, we prove that the suggested algorithms strongly converge to the minimum norm solution of the (SFP).

Highlights

IntroductionThe well-known convex feasibility problem is to find a point x∗ satisfying the following:
The well-known convex feasibility problem is to find a point x∗ satisfying the following:m x∗ ∈ Ci, i1 where m ≥ 1 is an integer, and each Ci is a nonempty closed convex subset of a Hilbert space H
The main purpose of this paper is to further investigate the regularized method 1.12

Summary

Introduction

The well-known convex feasibility problem is to find a point x∗ satisfying the following:. M x∗ ∈ Ci, i1 where m ≥ 1 is an integer, and each Ci is a nonempty closed convex subset of a Hilbert space H. A special case of the convex feasibility problem is the split feasibility problem SFP which is to find a point x∗ such that x∗ ∈ C, Ax∗ ∈ Q, Abstract and Applied Analysis where C and Q are two closed convex subsets of two Hilbert spaces H1 and H2, respectively, and A : H1 → H2 is a bounded linear operator. A special case of the SFP is the convexly constrained linear inverse problem 4 in the finite dimensional Hilbert spaces x∗ ∈ C, Ax∗ b

Objectives

Methods

Results