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Regularization Method for the Approximate Split Equality Problem in Infinite-Dimensional Hilbert Spaces

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  • Rudong Chen
  • Junlei Li
  • Yijie Ren

Abstract

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).

Suggested Citation

  • Rudong Chen & Junlei Li & Yijie Ren, 2013. "Regularization Method for the Approximate Split Equality Problem in Infinite-Dimensional Hilbert Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, May.
    • Handle: RePEc:hin:jnlaaa:813635
    DOI: 10.1155/2013/813635
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