- Title
- A counterexample to De Pierro's conjecture on the convergence of under-relaxed cyclic projections
- Creator
- Cominetti, Roberto; Roshchina, Vera; Williamson, Andrew
- Date
- 2019
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/168080
- Identifier
- vital:13769
- Identifier
-
https://doi.org/10.1080/02331934.2018.1474471
- Identifier
- ISBN:0233-1934
- Abstract
- The convex feasibility problem consists in finding a point in the intersection of a finite family of closed convex sets. When the intersection is empty, a best compromise is to search for a point that minimizes the sum of the squared distances to the sets. In 2001, de Pierro conjectured that the limit cycles generated by the ε-under-relaxed cyclic projection method converge when ε ↓ 0 towards a least squares solution. While the conjecture has been confirmed under fairly general conditions, we show that it is false in general by constructing a system of three compact convex sets in R3 for which the ε-under-relaxed cycles do not converge. © 2018 Informa UK Limited, trading as Taylor & Francis Group.
- Publisher
- Taylor and Francis Ltd.
- Relation
- Optimization Vol. 68, no. 1 (2019), p. 3-12
- Rights
- Copyright © 2018 Informa UK Limited, trading as Taylor & Francis Group.
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; Cyclic projections; De Pierro conjecture; Under-relaxed projections
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