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http://dx.doi.org/10.4134/CKMS.c150114

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)
Publication Information
Communications of the Korean Mathematical Society / v.31, no.4, 2016 , pp. 845-855 More about this Journal
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
p-uniformly convex metric space; p-resolvent map; proximal point algorithm;
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