Iterative algorithms with the regularization for the constrained convex minimization problem and maximal monotone operators

Optimization ◽  
2017 ◽  
Vol 66 (10) ◽  
pp. 1623-1646
Author(s):  
Wongvisarut Khuangsatung ◽  
Atid Kangtunyakarn
Keyword(s):  
Minimization Problem ◽  
Maximal Monotone ◽  
Iterative Algorithms ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Convex Minimization ◽  
Convex Minimization Problem ◽  
Constrained Convex Minimization ◽  
Constrained Convex Minimization Problem

scholarly journals Strong Convergence of Modified Algorithms Based on the Regularization for the Constrained Convex Minimization Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Ming Tian ◽  
Jun-Ying Gong
Keyword(s):  
Minimization Problem ◽  
Iterative Algorithms ◽  
Split Feasibility Problem ◽  
Convex Minimization ◽  
Feasibility Problem ◽  
Convex Minimization Problem ◽  
Constrained Convex Minimization ◽  
Constrained Convex Minimization Problem ◽  
The Split Feasibility Problem ◽  
Implicit And Explicit

As is known, the regularization method plays an important role in solving constrained convex minimization problems. Based on the idea of regularization, implicit and explicit iterative algorithms are proposed in this paper and the sequences generated by the algorithms can converge strongly to a solution of the constrained convex minimization problem, which also solves a certain variational inequality. As an application, we also apply the algorithm to solve the split feasibility problem.

scholarly journals Strong and Weak Convergence of Modified Mann Iteration for New Resolvents of Maximal Monotone Operators in Banach Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-20 ◽  
Author(s):  
Somyot Plubtieng ◽  
Wanna Sriprad
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Convergence Rate ◽  
Minimization Problem ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Convex Minimization Problem ◽  
Mann Iteration ◽  
Strong And Weak Convergence

We prove strong and weak convergence theorems for a new resolvent of maximal monotone operators in a Banach space and give an estimate of the convergence rate of the algorithm. Finally, we apply our convergence theorem to the convex minimization problem. The result present in this paper extend and improve the corresponding result of Ibaraki and Takahashi (2007), and Kim and Xu (2005).

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