Convergence analysis of the augmented Lagrangian method for nonlinear second-order cone optimization problems

2007 ◽  
Vol 67 (5) ◽  
pp. 1359-1373 ◽  
Author(s):  
Yong-Jin Liu ◽  
Li-Wei Zhang
Keyword(s):  
Convergence Analysis ◽  
Augmented Lagrangian ◽  
Optimization Problems ◽  
Augmented Lagrangian Method ◽  
Lagrangian Method ◽  
Second Order ◽  
Second Order Cone

Alternating direction based method for optimal control problem constrained by Stokes equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yu Gao ◽  
Jingzhi Li ◽  
Yongcun Song ◽  
Chao Wang ◽  
Kai Zhang
Keyword(s):  
Optimal Control ◽  
Discrete System ◽  
Augmented Lagrangian ◽  
Stokes Equations ◽  
Optimization Problems ◽  
Augmented Lagrangian Method ◽  
Lagrangian Method ◽  
The Finite Element Method ◽  
Alternating Direction ◽  
Different Types

Abstract We consider the optimal control problems constrained by Stokes equations. It has been shown in the literature, the problem can be discretized by the finite element method to generate a discrete system, and the error estimate has also been established. In this paper, we focus on solving the discrete system by the alternating splitting augmented Lagrangian method, which is a direct extension of alternating direction method of multipliers and possesses a global O ⁢ ( 1 / k ) \mathcal{O}({1}/{k}) convergence rate. In addition, we propose an acceleration scheme based on the alternating splitting augmented Lagrangian method to improve the efficiency of the algorithm. The error estimates and convergence analysis of our algorithms are presented for several different types of optimization problems. Finally, numerical experiments are performed to verify the efficiency of the algorithms.

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