A Proximal Point Method in Nonreflexive Banach Spaces

2009 ◽  
Vol 18 (1) ◽  
pp. 109-120 ◽  
Author(s):  
Alfredo N. Iusem ◽  
Elena Resmerita
Keyword(s):  
Banach Spaces ◽  
Point Method ◽  
Proximal Point Method ◽  
Proximal Point

scholarly journals A proximal point method for nonsmooth convex optimization problems in Banach spaces

1997 ◽  
Vol 2 (1-2) ◽  
pp. 97-120 ◽  
Author(s):  
Y. I. Alber ◽  
R. S. Burachik ◽  
A. N. Iusem
Keyword(s):  
Banach Space ◽  
Convex Optimization ◽  
Banach Spaces ◽  
Optimization Problems ◽  
Geometric Characteristic ◽  
Point Method ◽  
Proximal Point Method ◽  
Projection Operators ◽  
Proximal Point ◽  
Generalized Projection Operators

In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the dual Banach space, namely its modulus of convexity. We apply a new technique which includes Banach space geometry, estimates of duality mappings, nonstandard Lyapunov functionals and generalized projection operators in Banach spaces.

On a Bregman regularized proximal point method for solving equilibrium problems

2019 ◽  
Vol 13 (5) ◽  
pp. 1143-1155
Author(s):  
J. X. Cruz Neto ◽  
P. S. M. Santos ◽  
R. C. M. Silva ◽  
J. C. O. Souza
Keyword(s):  
Equilibrium Problems ◽  
Point Method ◽  
Proximal Point Method ◽  
Proximal Point
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