The Composition of Projections onto Closed Convex Sets in Hilbert Space Is Asymptotically Regular

  title={The Composition of Projections onto Closed Convex Sets in Hilbert Space Is Asymptotically Regular},
  author={Heinz H. Bauschke},
The composition of finitely many projections onto closed convex sets in Hilbert space arises naturally in the area of projection algorithms. We show that this composition is asymptotically regular, thus proving the socalled “zero displacement conjecture” of Bauschke, Borwein and Lewis. The proof relies on a rich mix of results from monotone operator theory, fixed point theory, and convex analysis. 1. The problem We assume that X is a real Hilbert space with inner product 〈·, ·〉, and that C1… CONTINUE READING


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