Battistoni, F., Daniilidis, A., De Bernardi, C. A., & Miglierina, E. (2025). Characterization of regularity via variational stability of alternating projections sequences. arXiv. https://doi.org/10.48550/arXiv.2511.07953
The notion of regular pair (A,B) for two non empty closed convex subsets A and B of a Hilbertspace H was introduced by Borwein and Bauschke in 1993 to ensure convergence (innorm) of the alternating projection method to some point of the best approximation set. In 2022, De Bernardi and Miglierina showed that regularity of the pair (A,B) guarantees, additionally, the convergence for any variational perturbation of the alternating projection method, provided the corresponding best approximation sets are bounded. The aim of this paper is to show that the converse assertion is also true.
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Project title:
Unilateralität und Asymmetrie in der Variationsanalyse: P 36344N (FWF - Österr. Wissenschaftsfonds)
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Project (external):
INdAM GNAMPA INdAM GNAMPA MICINN
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Project ID:
Professore Visitatore CUP E53C23001670001 PID2020-112491GB-I00
