- There is no variational characterization of the cycles in the method of periodic projections J.-B. Baillon(Jean-Bernard.Baillonuniv-paris1.fr) P. L. Combettes(plcmath.jussieu.fr) R. Cominetti(rcccdii.uchile.cl) Abstract: 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. Keywords: projection algorithm, inconsistent feasibility problem, cycles, periodic projections Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Category 2: Infinite Dimensional Optimization Citation: Download: [PDF]Entry Submitted: 02/07/2011Entry Accepted: 02/07/2011Entry Last Modified: 02/07/2011Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society.