THE PROXIMAL POINT ALGORITHM IN UNIFORMLY CONVEX METRIC SPACES
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 proxim...
Gespeichert in:
| Veröffentlicht in: | Communications of the Korean Mathematical Society 2016, 31(4), , pp.845-855 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | 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. KCI Citation Count: 0 |
|---|---|
| ISSN: | 1225-1763 2234-3024 |
| DOI: | 10.4134/CKMS.c150114 |