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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/813635 |
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| Summary: | 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). |
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| ISSN: | 1085-3375 1687-0409 |