Modified proximal point algorithms on Hadamard manifolds

Abstract

Given a maximal monotone vector field A on a Hadamard manifold, we devise a modified proximal point algorithm which, under reasonable assumptions, converges to a singular point of A. This algorithm is a natural extension to the Hadamard manifold of the one introduced by Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc. 66 (2002), pp. 240–256 in Hilbert spaces.

Keywords:

• modified proximal point algorithms
• Hadamard manifold
• monotone vector field
• maximal monotone

AMS Subject Classifications::

• 47J25
• 47H05

Acknowledgements

The second author was partially supported by DGES, Grant MTM2006-13997-C02-01 and Junta de Andalucía, Grant FQM-127.