Steepest-descent proximal point algorithms for a class of variational inequalities in Banach spaces

2018 ◽  
Vol 291 (8-9) ◽  
pp. 1191-1207 ◽  
Author(s):  
Nguyen Buong
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Steepest Descent ◽  
Proximal Point ◽  
Proximal Point Algorithms

Generalized super-relaxed proximal point algorithms involving relative A-maximal relaxed accretive in Banach spaces

2014 ◽  
Vol 5 (2) ◽  
Author(s):  
Mohsen Alimohammady ◽  
Morteza K. Kalleji
Keyword(s):  
Banach Spaces ◽  
General Framework ◽  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Proximal Point Algorithms

Abstract.A general framework for a relaxed proximal point algorithm using the notion of

scholarly journals Proximal Point Algorithms for Finding a Zero of a Finite Sum of Monotone Mappings in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
H. Zegeye ◽  
N. Shahzad
Keyword(s):  
Banach Spaces ◽  
Minimization Problem ◽  
Iterative Process ◽  
Monotone Mappings ◽  
Important Class ◽  
Convex Minimization Problem ◽  
Proximal Point ◽  
Proximal Point Algorithms ◽  
Finite Sum ◽  
Nonlinear Mappings

We introduce an iterative process which converges strongly to a zero of a finite sum of monotone mappings under certain conditions. Applications to a convex minimization problem are included. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear mappings.

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