A Parallel Algorithm for Large Scale Optimal Control Problems Using Spatial Decomposition and Coordination * *The work was supported in part by the National Science Foundation under Grant ECS-8717167. The authors would like to thank Professor S. C. Chang of National Taiwan University for valuable comments.

1990 ◽  
Vol 23 (8) ◽  
pp. 143-148
Author(s):  
Xiaohong Guan ◽  
P.B. Luh
Keyword(s):  
Optimal Control ◽  
Parallel Algorithm ◽  
National Science Foundation ◽  
Large Scale ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Spatial Decomposition ◽  
Decomposition And Coordination ◽  
National Science

scholarly journals Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks

2020 ◽  
Vol 146 (2) ◽  
pp. 335-368
Author(s):  
Owe Axelsson ◽  
János Karátson
Keyword(s):  
Optimal Control ◽  
Rate Of Convergence ◽  
Large Scale ◽  
Optimal Control Problems ◽  
Iterative Solution ◽  
Control Problems ◽  
Block Form ◽  
Solution Methods ◽  
Preconditioned Matrix ◽  
Iterative Solution Methods

Abstract Matrices or operators in two-by-two block form with square blocks arise in numerous important applications, such as in optimal control problems for PDEs. The problems are normally of very large scale so iterative solution methods must be used. Thereby the choice of an efficient and robust preconditioner is of crucial importance. Since some time a very efficient preconditioner, the preconditioned square block, PRESB method has been used by the authors and coauthors in various applications, in particular for optimal control problems for PDEs. It has been shown to have excellent properties, such as a very fast and robust rate of convergence that outperforms other methods. In this paper the fundamental and most important properties of the method are stressed and presented with new and extended proofs. Under certain conditions, the condition number of the preconditioned matrix is bounded by 2 or even smaller. Furthermore, under certain assumptions the rate of convergence is superlinear.

scholarly journals Decomposition of large-scale stochastic optimal control problems

2010 ◽  
Vol 44 (3) ◽  
pp. 167-183 ◽  
Author(s):  
Kengy Barty ◽  
Pierre Carpentier ◽  
Pierre Girardeau
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Large Scale ◽  
Optimal Control Problems ◽  
Control Problems
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