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Stability of a convex feasibility problem

Author

Listed:
  • Carlo Alberto Bernardi

    (Università Cattolica del Sacro Cuore)

  • Enrico Miglierina

    (Università Cattolica del Sacro Cuore)

  • Elena Molho

    (Università degli Studi di Pavia)

Abstract

The 2-sets convex feasibility problem aims at finding a point in the intersection of two closed convex sets A and B in a normed space X. More generally, we can consider the problem of finding (if possible) two points in A and B, respectively, which minimize the distance between the sets. In the present paper, we study some stability properties for the convex feasibility problem: we consider two sequences of sets, each of them converging, with respect to a suitable notion of set convergence, respectively, to A and B. Under appropriate assumptions on the original problem, we ensure that the solutions of the perturbed problems converge to a solution of the original problem. We consider both the finite-dimensional and the infinite-dimensional case. Moreover, we provide several examples that point out the role of our assumptions in the obtained results.

Suggested Citation

  • Carlo Alberto Bernardi & Enrico Miglierina & Elena Molho, 2019. "Stability of a convex feasibility problem," Journal of Global Optimization, Springer, vol. 75(4), pages 1061-1077, December.
    • Handle: RePEc:spr:jglopt:v:75:y:2019:i:4:d:10.1007_s10898-019-00806-w
    DOI: 10.1007/s10898-019-00806-w
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    Cited by:

    1. Md Saiful Islam & Md Sarowar Morshed & Md. Noor-E-Alam, 2022. "A Computational Framework for Solving Nonlinear Binary Optimization Problems in Robust Causal Inference," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3023-3041, November.
    2. Carlo Alberto Bernardi & Enrico Miglierina, 2021. "A variational approach to the alternating projections method," Journal of Global Optimization, Springer, vol. 81(2), pages 323-350, October.

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