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2013 Regularization Method for the Approximate Split Equality Problem in Infinite-Dimensional Hilbert Spaces
Rudong Chen, Junlei Li, Yijie Ren
Abstr. Appl. Anal. 2013(SI01): 1-5 (2013). DOI: 10.1155/2013/813635

Abstract

We studied the approximate split equality problem (ASEP) in the framework of infinite-dimensional Hilbert spaces. Let H 1 , H 2 , and H 3 be infinite-dimensional real Hilbert spaces, let C H 1 and Q H 2 be two nonempty closed convex sets, and let A : H 1 H 3 and B : H 2 H 3 be two bounded linear operators. The ASEP in infinite-dimensional Hilbert spaces is to minimize the function f x , y = (1 / 2) A x - B y 2 2 over x C and y Q . Recently, Moudafi and Byrne had proposed several algorithms for solving the split equality problem and proved their convergence. Note that their algorithms have only weak convergence in infinite-dimensional Hilbert spaces. In this paper, we used the regularization method to establish a single-step iterative for solving the ASEP in infinite-dimensional Hilbert spaces and showed that the sequence generated by such algorithm strongly converges to the minimum-norm solution of the ASEP. Note that, by taking B = I in the ASEP, we recover the approximate split feasibility problem (ASFP).

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Rudong Chen. Junlei Li. Yijie Ren. "Regularization Method for the Approximate Split Equality Problem in Infinite-Dimensional Hilbert Spaces." Abstr. Appl. Anal. 2013 (SI01) 1 - 5, 2013. https://doi.org/10.1155/2013/813635

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1278.90442
MathSciNet: MR3049423
Digital Object Identifier: 10.1155/2013/813635

Rights: Copyright © 2013 Hindawi

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