2011/02/07 by Baillon, J. -B., Combettes, P. L., Cominetti, R. · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1102.1378
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≥ 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.