Hybrid inexact proximal point algorithms based on RMM frameworks with applications to variational inclusion problems

2011 ◽  
Vol 39 (1-2) ◽  
pp. 345-365 ◽  
Author(s):  
Ram U. Verma
Keyword(s):  
Variational Inclusion ◽  
Proximal Point ◽  
Inclusion Problems ◽  
Proximal Point Algorithms ◽  
Inexact Proximal ◽  
Inexact Proximal Point Algorithms

scholarly journals Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis

2009 ◽  
Vol 2009 ◽  
pp. 1-11
Author(s):  
Ram U. Verma
Keyword(s):  
Convergence Analysis ◽  
Proximal Point Algorithm ◽  
Evolution Equations ◽  
Real Hilbert Space ◽  
Linear Convergence ◽  
Proximal Point ◽  
Evolution Inclusions ◽  
Inclusion Problems ◽  
Set Valued Mapping ◽  
Inexact Proximal

Based on a notion ofrelatively maximal(m)-relaxed monotonicity, the approximation solvability of a general class of inclusion problems is discussed, while generalizing Rockafellar's theorem (1976) on linear convergence using the proximal point algorithm in a real Hilbert space setting. Convergence analysis, based on this new model, is simpler and compact than that of the celebrated technique of Rockafellar in which the Lipschitz continuity at 0 of the inverse of the set-valued mapping is applied. Furthermore, it can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution equations as well as evolution inclusions.

Sign in / Sign up

Export Citation Format

Share Document