Two modified proximal point algorithms in geodesic spaces with curvature bounded above

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Abstract

We obtain existence and convergence theorems for two variants of the proximal point algorithm involving proper lower semicontinuous convex functions in complete geodesic spaces with curvature bounded above.

Keywords

\(\text {CAT}(1)\) space Convex function Fixed point Geodesic space Minimizer Proximal point algorithm Resolvent 

Mathematics Subject Classification

Primary 52A41 90C25 Secondary 47H10 47J05 

Notes

Acknowledgements

The authors would like to thank the anonymous referees for their helpful comments on the original version of this paper. This work was supported by JSPS KAKENHI Grant Numbers 15K05007 and 17K05372.

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Information ScienceToho UniversityMiyama, FunabashiJapan
  2. 2.Department of Mathematical SciencesTokai UniversityKitakaname, HiratsukaJapan

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