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THE PROXIMAL POINT ALGORITHM IN UNIFORMLY CONVEX METRIC SPACES

  • Choi, Byoung Jin (Department of Mathematics Sungkyunkwan University) ;
  • Ji, Un Cig (Department of Mathematics Research Institute of Mathematical Finance Chungbuk National University)
  • Received : 2015.06.16
  • Published : 2016.10.31

Abstract

We introduce the proximal point algorithm in a p-uniformly convex metric space. We first introduce the notion of p-resolvent map in a p-uniformly convex metric space as a generalization of the Moreau-Yosida resolvent in a CAT(0)-space, and then we secondly prove the convergence of the proximal point algorithm by the p-resolvent map in a p-uniformly convex metric space.

Keywords

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