Daniilidis, A. (2026). Alternating projections: self-contractedness and variational stability. In Workshop in Geometric and Functional Analysis - Book of Abstracts (pp. 7–7).
Alternate projection method is a classical approach to deal with the convex feasibility problem. In this talk we show that given two nonempty closed convex sets A and B, the consecutive projections xn+1 = PB(PA(xn)), n ≥ 1 produce a self-contacted sequence (ensuring an explicit asymptotic behavior and an alternative way to establish convergence in the finite dimensional case). We also study the variational stability of the above method in a Hilbert space setting and discuss the state-of-the-art.
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Project title:
Unilateralität und Asymmetrie in der Variationsanalyse: P 36344N (FWF - Österr. Wissenschaftsfonds)
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Additional information:
A. Böhm, A. Daniilidis, Ubiquitous algorithms in convex optimization generate self-contracted sequences, J. Convex Anal. 29 (2022) 119–128.
F. Battistoni, C. De Bernardi, A. Daniilidis, E. Miglierina Characterizations of regularity via variational stability of alternating projections sequences, arXiv 2511.97853 (preprint 16p, 2025)
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Research Areas:
Mathematical and Algorithmic Foundations: 20% Fundamental Mathematics Research: 80%
