On the Relation Between Bundle Methods for Maximal Monotone Inclusions and Hybrid Proximal Point Algorithms

2001 ◽  
pp. 441-455 ◽  
Author(s):  
Claudia A. Sagastizábal ◽  
Mikhail V. Solodov
Keyword(s):  
Maximal Monotone ◽  
Bundle Methods ◽  
Proximal Point ◽  
Proximal Point Algorithms ◽  
Monotone Inclusions

scholarly journals A Proximal Point Method Involving Two Resolvent Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Oganeditse A. Boikanyo
Keyword(s):  
Hilbert Space ◽  
Proximal Point Algorithm ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Proximal Point Method ◽  
Resolvent Operators ◽  
Proximal Point ◽  
Proximal Point Algorithms ◽  
Frame Work

We construct a sequence of proximal iterates that converges strongly (under minimal assumptions) to a common zero of two maximal monotone operators in a Hilbert space. The algorithm introduced in this paper puts together several proximal point algorithms under one frame work. Therefore, the results presented here generalize and improve many results related to the proximal point algorithm which were announced recently in the literature.

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