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Solving Nonconvex Feasibility Problem on a Sphere and a Closed Ball by Douglas–Rachford Algorithm

Author

Listed:
  • Kumari Sweta Srivastava

    (Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha 769008, India)

  • S. R. Pattanaik

    (Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha 769008, India)

Abstract

In recent times, a variety of nonconvex feasibility problems have been solved empirically by employing Douglas–Rachford (DR) splitting methods. However, this theory is not adequate in explaining the observed success and is more concerned with the local convergence. In this paper, we study the convergence of the DR splitting method for finding a point of intersection of a closed ball and a sphere in the n-dimensional Euclidean spaces. Also, we provide the region for the global convergence of the DR splitting method.

Suggested Citation

  • Kumari Sweta Srivastava & S. R. Pattanaik, 2021. "Solving Nonconvex Feasibility Problem on a Sphere and a Closed Ball by Douglas–Rachford Algorithm," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 38(01), pages 1-20, February.
    • Handle: RePEc:wsi:apjorx:v:38:y:2021:i:01:n:s0217595920500426
    DOI: 10.1142/S0217595920500426
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