Proximal Point Algorithm for Quasi-convex Minimization Problems in metric spaces
Functional Analysis
2016-11-08 v1
Abstract
In this paper, the proximal point algorithm for quasi-convex minimization problem in nonpositive curvature metric spaces is studied. We prove -convergence of the generated sequence to a critical point (which is defined in the text) of an objective convex, proper and lower semicontinuous function with at least a minimum point as well as some strong convergence results to a minimum point with some additional conditions. The results extend the recent results of the proximal point algorithm in Hadamard manifolds and CAT(0) spaces.
Cite
@article{arxiv.1611.01830,
title = {Proximal Point Algorithm for Quasi-convex Minimization Problems in metric spaces},
author = {Hadi Khatibzadeh and Vahid Mohebbi},
journal= {arXiv preprint arXiv:1611.01830},
year = {2016}
}