There is no variational characterization of the cycles in the method of periodic projections
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| Format: | Preprint |
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2011
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| _version_ | 1866917274815823872 |
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| author | Baillon, J. -B. Combettes, P. L. Cominetti, R. |
| author_facet | Baillon, J. -B. Combettes, P. L. Cominetti, R. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1102_1378 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | There is no variational characterization of the cycles in the method of periodic projections Baillon, J. -B. Combettes, P. L. Cominetti, R. Functional Analysis 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. |
| title | There is no variational characterization of the cycles in the method of periodic projections |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/1102.1378 |