﻿ 带稀疏约束的分裂可行问题的算法 The Solution of Sparsity-Constrained Split Feasibility Problem

Vol.05 No.02(2016), Article ID:17660,7 pages
10.12677/AAM.2016.52034

The Solution of Sparsity-Constrained Split Feasibility Problem

Hanxiao Chang, Jun Sun, Biao Qu

School of Management, Qufu Normal University, Rizhao Shandong

Received: May 4th, 2016; accepted: May 23rd, 2016; published: May 26th, 2016

ABSTRACT

In this paper, we mainly study the solution of sparsity-constrained split feasibility problem. Under some reasonable assumptions, we use IHT algorithm to get the stationary points of sparsity-constrained split feasibility problem and get a conclusion which plays an important role in local convergence analysis.

Keywords:Split Feasible Problem, Sparsity-Constrained, IHT Algorithm, Stationery

1. 引言

, (1.2)

, , 使得 (1.3)

(1.4)

2. 预备知识

2.1. 支撑映射

,

2.2. L-稳定点

(2.1)

2.3. 导集

(2.2)

(2.3)

(2.4)

(2.5)

(1)是一个-稳定点。

(2)为一个单点集。

3. IHT算法

(1)

(2)是一个不增数列；

(3)

(2.6)

。因为都收敛到，所以存在使得当时，有：

，故存在的子列使得：

(2.7)

(2.8)

，由引理3.1的(3)和(2.7)式知，使得：

(2.9)

(2.10)

(2.11)

(2.12)

(2.13)

4. 总结

The Solution of Sparsity-Constrained Split Feasibility Problem[J]. 应用数学进展, 2016, 05(02): 269-275. http://dx.doi.org/10.12677/AAM.2016.52034

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