Affine subspace – 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

The best approximation pair problem relative to two subsets in a normed space

Published: 2024/04/04, Updated: 2025/09/04

Convex and Nonsmooth Optimization, Global Optimization, Infinite Dimensional Optimization Affine subspace, best approximation pair (BAP), existence of a BAP, normed space, parallel intervals, reflexive Banach space, strictly convex, uniqueness of a BAP, weakly sequentially compact

In the classical best approximation pair (BAP) problem, one is given two nonempty, closed, convex and disjoint subsets in a finite- or an infinite-dimensional Hilbert space, and the goal is to find a pair of points, each from each subset, which realizes the distance between the subsets. We discuss the problem in more general normed … Read more