Document Type
Report
Source Publication Title
Technical Report 318
Abstract
We analyze the behavior of a parallel proximal point method for solving convex optimization problems in reflexive Banach spaces. Similar algorithms were known to converge under the implicit assumption that the norm of the space is Hilbertian. We extend the area of applicability of the proximal point method to solving convex optimization problems in Banach spaces on which totally convex functions can be found. This includes the class of all smooth uniformly convex Banach spaces. Also, our convergence results leave more flexibility for the choice of the penalty function involved in the algorithm and, in this way, allow simplification of the computational procedure.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
2-1-1997
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Iusem, Alfredo N. and Butnariu, Dan, "On a Proximal Point Method for Optimization in Banach Spaces" (1997). Mathematics Technical Papers. 344.
https://mavmatrix.uta.edu/math_technicalpapers/344