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The Split Feasibility Problem and Its Solution Algorithm

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  • Biao Qu
  • Binghua Liu

Abstract

The split feasibility problem arises in many fields in the real world, such as signal processing, image reconstruction, and medical care. In this paper, we present a solution algorithm called memory gradient projection method for solving the split feasibility problem, which employs a parameter and two previous iterations to get the next iteration, and its step size can be calculated directly. It not only improves the flexibility of the algorithm, but also avoids computing the largest eigenvalue of the related matrix or estimating the Lipschitz constant in each iteration. Theoretical convergence results are established under some suitable conditions.

Suggested Citation

  • Biao Qu & Binghua Liu, 2018. "The Split Feasibility Problem and Its Solution Algorithm," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-7, January.
    • Handle: RePEc:hin:jnlmpe:4123168
    DOI: 10.1155/2018/4123168
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