scholarly journals Tight Global Linear Convergence Rate Bounds for Operator Splitting Methods

2018 ◽  
Vol 63 (12) ◽  
pp. 4126-4139 ◽  
Author(s):  
Goran Banjac ◽  
Paul J. Goulart
Keyword(s):  
Convergence Rate ◽  
Operator Splitting ◽  
Linear Convergence ◽  
Splitting Methods ◽  
Linear Convergence Rate ◽  
Global Linear Convergence ◽  
Operator Splitting Methods

scholarly journals Convergence rate analysis of an iterative algorithm for solving the multiple-sets split equality problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shijie Sun ◽  
Meiling Feng ◽  
Luoyi Shi
Keyword(s):  
Convergence Rate ◽  
Iterative Algorithm ◽  
Sufficient Conditions ◽  
Linear Convergence ◽  
Regularity Property ◽  
Step Size ◽  
Bounded Linear ◽  
Split Equality Problem ◽  
Linear Convergence Rate ◽  
Equality Problem

Abstract This paper considers an iterative algorithm of solving the multiple-sets split equality problem (MSSEP) whose step size is independent of the norm of the related operators, and investigates its sublinear and linear convergence rate. In particular, we present a notion of bounded Hölder regularity property for the MSSEP, which is a generalization of the well-known concept of bounded linear regularity property, and give several sufficient conditions to ensure it. Then we use this property to conclude the sublinear and linear convergence rate of the algorithm. In the end, some numerical experiments are provided to verify the validity of our consequences.

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