Yasunori Kimura, Fumiaki Kohsaka
Published 2017-04-19Version 1
We investigate the asymptotic behavior of sequences generated by the proximal point algorithm for convex functions in complete geodesic spaces with curvature bounded above. Using the notion of resolvents of such functions, which was recently introduced by the authors, we show the existence of minimizers of convex functions under the boundedness assumptions on such sequences as well as the convergence of such sequences to minimizers of given functions.
Comments: Accepted for publication in the journal Linear and Nonlinear Analysis (Submitted on 4 August 2016; Revised on 29 September 2016). arXiv admin note: text overlap with arXiv:1704.01360
Two modified proximal point algorithms in geodesic spaces with curvature bounded above
Existence and approximation of fixed points of vicinal mappings in geodesic spaces
The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces
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