Asymptotic Convergence Analysis of a New Class of Proximal Point Methods

2007 ◽  
Vol 46 (5) ◽  
pp. 1683-1704 ◽  
Author(s):  
William W. Hager ◽  
Hongchao Zhang
Keyword(s):  
Convergence Analysis ◽  
Asymptotic Convergence ◽  
Proximal Point ◽  
Proximal Point Methods ◽  
New Class

Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds

2020 ◽  
Vol 186 (3) ◽  
pp. 879-898
Author(s):  
Erik Alex Papa Quiroz ◽  
Nancy Baygorrea Cusihuallpa ◽  
Nelson Maculan
Keyword(s):  
Hadamard Manifolds ◽  
Proximal Point ◽  
Proximal Point Methods ◽  
Inexact Proximal

Modified proximal point algorithms involving convex combination technique for solving minimization problems with convergence analysis

Optimization ◽  
2019 ◽  
Vol 69 (7-8) ◽  
pp. 1655-1680 ◽  
Author(s):  
Nopparat Wairojjana ◽  
Nuttapol Pakkaranang ◽  
Izhar Uddin ◽  
Poom Kumam ◽  
Aliyu Muhammed Awwal
Keyword(s):  
Convergence Analysis ◽  
Convex Combination ◽  
Proximal Point ◽  
Proximal Point Algorithms ◽  
Combination Technique ◽  
Minimization Problems

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.

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