half-space – Optimization Online

On the boundedness of infinite products of relaxed projections: perturbations resilience and dynamic string-averaging

Published: 2026/07/29

Basic Sciences Applications, Convex Optimization, Infinite Dimensional Optimization Affine subspace, boundedness, control, dynamic string-averaging, half-space, infinite product, innately regular, perturbation resilience, relaxed projection, strongly nonexpansive mapping

Very recently (2026), Bauschke and Tung extended from finite- to infinite-dimensional Hilbert spaces a result published by Meshulam in 1996 (following an earlier result of Aharoni-Duchet-Wajnryb from 1984) regarding the boundedness of infinite products of relaxed projections onto a finite family of closed affine subspaces. In the present note we extend in various ways the … Read more

Modified alternating direction methods for the modified multiple-sets split feasibility problems

Published: 2012/10/09

Complementarity and Variational Inequalities alternating direction method, convergence rate, half-space, multiple-sets split feasibility problem, parallel computing

Inthispaper, weproposetwonewmultiple-setssplitfeasibilityproblem(MSFP)models, where the MSFP requires to find a point closest to the intersection of a family of closed convex sets in one space, such that its image under a linear transformation will be closest to the intersection of another family of closed convex sets in the image space. This problem arises in image restoration, … Read more