An alternating projection that does not converge in norm

By Hein Hundal. 2004

146 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/753377c78afaa5bce01f900f35f43f8a1fa377d1

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In Computational Theory and Mathematics

In Geometry and Topology

In Numerical Analysis

Citations in the corpus

Single projection method for pseudo-monotone variational inequality in Hilbert spaces (2018, result): “coincides with {xn} generated by Hundal in [44], which shows that {xn} converges weakly, but not strongly as proved by Hundal [44].”
Strong asymptotic convergence of evolution equations governed by maximal monotone operators with Tikhonov regularization (2008, background): “More examples of this kind have appeared recently in [8,9], based on results of [23].”
Alternating projections in CAT(0) spaces (2011, background): “A decades-old problem as to whether or not the convergence of (1) has to be in norm was answered quite recently in the negative [19].”
Projection and proximal point methods: convergence results and counterexamples (2004, background): “Ever since, there has been a nagging gap between von Neumann’s and Bregman’s result: Is it possible that norm convergence fails? In 2000, Hundal announced his affirmative answer to this question; full details of his ingenious construction became available two years later, see [34].”
A new proximal point iteration that converges weakly but not in norm (2005, background): “Hundal recently answered this question in the negative [10]:”
A Dykstra-like algorithm for two monotone operators (2007, background): “Unfortunately, this result fails in two respects when U and V are general intersecting closed convex sets: first, while weak convergence of the sequences (xn)n∈N and (yn)n∈N in (1) holds [8], strong convergence can fail [16]; second, as simple examples show [9], the limit point need not be the proje”
Fitzpatrick functions, cyclic monotonicity and Rockafellar's antiderivative (2007, methodology): “Using an ingenious construction by Hundal [26] (see also [30]), the authors of [6] gave an affirmative answer to this question.”
Weak convergence of infinite products of operators in Hadamard spaces (2016, background): “Thus Hundal’s counterexample (see [14] and [18]) gives us a CAT(0) space for which, under the assumptions of Corollary 3.”