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Author (up) Cominetti, R.; Roshchina, V.; Williamson, A. doi  openurl
  Title A counterexample to De Pierro's conjecture on the convergence of under-relaxed cyclic projections Type Journal Article
  Year 2019 Publication Optimization Abbreviated Journal Optimization  
  Volume 68 Issue 1 Pages 3-12  
  Keywords Cyclic projections; under-relaxed projections; De Pierro conjecture  
  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 -under-relaxed cyclic projection method converge when 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 for which the -under-relaxed cycles do not converge.  
  Address [Cominetti, Roberto] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: v.roshchina@unsw.edu.au  
  Corporate Author Thesis  
  Publisher Taylor & Francis Ltd Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0233-1934 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000459733300002 Approved no  
  Call Number UAI @ eduardo.moreno @ Serial 987  
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