An SOR implicit iterative algorithm for coupled Lyapunov equations

Automatica ◽  
2018 ◽  
Vol 97 ◽  
pp. 38-47 ◽  
Author(s):  
Ai-Guo Wu ◽  
Hui-Jie Sun ◽  
Ying Zhang
Keyword(s):  
Iterative Algorithm ◽  
Lyapunov Equations ◽  
Implicit Iterative Algorithm

scholarly journals Iterative Schemes for Convex Minimization Problems with Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Cheng-Wen Liao ◽  
Chin-Tzong Pang ◽  
Ching-Feng Wen
Keyword(s):  
Strong Convergence ◽  
Iterative Algorithm ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Generalized Mixed Equilibrium Problem ◽  
Strong Convergence Theorem ◽  
Generalized Mixed Equilibrium ◽  
Generalized Equilibrium ◽  
Fréchet Differentiable ◽  
Implicit Iterative Algorithm

We first introduce and analyze one implicit iterative algorithm for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: the generalized mixed equilibrium problem, the system of generalized equilibrium problems, and finitely many variational inclusions in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another implicit iterative algorithm for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions.

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