Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013, Special Issue (2013), Article ID 813635, 5 pages.
Regularization Method for the Approximate Split Equality Problem in Infinite-Dimensional Hilbert Spaces
We studied the approximate split equality problem (ASEP) in the framework of infinite-dimensional Hilbert spaces. Let , , and be infinite-dimensional real Hilbert spaces, let and be two nonempty closed convex sets, and let and be two bounded linear operators. The ASEP in infinite-dimensional Hilbert spaces is to minimize the function over and . 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 in the ASEP, we recover the approximate split feasibility problem (ASFP).
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 813635, 5 pages.
First available in Project Euclid: 26 February 2014
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Chen, Rudong; Li, Junlei; Ren, Yijie. Regularization Method for the Approximate Split Equality Problem in Infinite-Dimensional Hilbert Spaces. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 813635, 5 pages. doi:10.1155/2013/813635. https://projecteuclid.org/euclid.aaa/1393444394