Modified proximal point algorithms on Hadamard manifolds

Author： Wang Jin-Hua  

Publisher： Taylor & Francis Ltd

ISSN： 0233-1934

Source： Optimization, Vol.60, Iss.6, 2011-06, pp. : 697-708

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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.

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