Applied Mathematics Colloquium

Hundal's alternating projections counterexample and the proximal point algorithm

Heinz Bauschke

Department of Mathematics and Statistics
University of Guelph

Abstract

Hein Hundal recently constructed an alternating projections iteration that converges weakly but not in norm. In this talk, I will show how Hundal's example can be viewed as a sequence, generated by the proximal point algorithm, that converges weakly but not in norm. The existence of such a sequence was first established by Osman Guler; however, the construction proposed here is much simpler.

Based on joint works with J. Burke, F. Deutsch, H. Hundal, E. Matouskova, S. Reich, and J. Vanderwerff.