Approximation methods for nonexpansive type mappings in Hadamard manifolds. (English) Zbl 1251.47058
Bauschke, Heinz H. (ed.) et al., Fixed-point algorithms for inverse problems in science and engineering. Based on the presentations at the interdisciplinary workshop, BIRS, Banff, Canada, November 1–6, 2009. New York, NY: Springer (ISBN 978-1-4419-9568-1/hbk; 978-1-4419-9569-8/ebook). Springer Optimization and Its Applications 49, 273-299 (2011).
A Hadamard manifold is a simply connected complete Riemannian manifold of nonpositive sectional curvature (thus diffeomorphic to Euclidean space via the exponential map). The authors survey some results on nonexpansive maps on Hadamard manifolds. There are no proofs, but one numerical example comparing the Mann and the Halpern iteration scheme.
For the entire collection see [Zbl 1217.00018].
For the entire collection see [Zbl 1217.00018].
Reviewer: Christian Fenske (Gießen)
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 58C30 | Fixed-point theorems on manifolds |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H14 | Perturbations of nonlinear operators |
| 65K05 | Numerical mathematical programming methods |
| 90C25 | Convex programming |
Keywords:
Hadamard manifold; fixed point; nonexpansive mapping; set-valued vector field; monotone vector fieldReferences:
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