Year: 2025
Type: article
Abstract: We provide new conditions under which the alternating projection sequence converges in norm for the convex feasibility problem where a linear subspace with finite codimension N ≥ 2 N\geq 2 and a lattice cone in a Hilbert space are considered. The first result holds for any Hilbert lattice, assuming that the orthogonal complement of the linear subspace admits a basis made by disjoint vectors with respect to the lattice structure. The second result is specific for ℓ 2 ( N ) \ell ^2(\mathbb {N}) and is proved when only one vector of the basis is not in the cone but the sign of its components is definitively constant and its support has finite intersection with the supports of the remaining vectors.
DOI: 10.1090/proc/17373
Authors: Francesco Battistoni, Enrico Miglierina
Institution: Università Cattolica del Sacro Cuore
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415620161