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Finding best approximation pairs for two intersections of closed convex sets

Author

Listed:
  • Heinz H. Bauschke

    (University of British Columbia)

  • Shambhavi Singh

    (University of British Columbia)

  • Xianfu Wang

    (University of British Columbia)

Abstract

The problem of finding a best approximation pair of two sets, which in turn generalizes the well known convex feasibility problem, has a long history that dates back to work by Cheney and Goldstein in 1959. In 2018, Aharoni, Censor, and Jiang revisited this problem and proposed an algorithm that can be used when the two sets are finite intersections of halfspaces. Motivated by their work, we present alternative algorithms that utilize projection and proximity operators. Our modeling framework is able to accommodate even convex sets. Numerical experiments indicate that these methods are competitive and sometimes superior to the one proposed by Aharoni et al.

Suggested Citation

  • Heinz H. Bauschke & Shambhavi Singh & Xianfu Wang, 2022. "Finding best approximation pairs for two intersections of closed convex sets," Computational Optimization and Applications, Springer, vol. 81(1), pages 289-308, January.
    • Handle: RePEc:spr:coopap:v:81:y:2022:i:1:d:10.1007_s10589-021-00324-0
    DOI: 10.1007/s10589-021-00324-0
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