There is no variational characterization of the cycles in the method of periodic projections

Details There is no variational characterization of the cycles in the method of periodic projections There is no variational characterization of the cycles in the method of periodic projections

2011-02-07

arxiv.org/abs/1102.1378v1

Mathematics

Functional Analysis

Scientific paper

The method of periodic projections consists in iterating projections onto $m$ closed convex subsets of a Hilbert space according to a periodic sweeping strategy. In the presence of $m\geq 3$ sets, a long-standing question going back to the 1960s is whether the limit cycles obtained by such a process can be characterized as the minimizers of a certain functional. In this paper we answer this question in the negative. Projection algorithms that minimize smooth convex functions over a product of convex sets are also discussed.

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