Primal-Dual Active Set Strategy for a General Class of Constrained Optimal Control Problems

2002 ◽  
Vol 13 (2) ◽  
pp. 321-334 ◽  
Author(s):  
K. Kunisch ◽  
A. Rösch
Keyword(s):  
Optimal Control ◽  
General Class ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Active Set ◽  
Constrained Optimal Control ◽  
Active Set Strategy ◽  
Primal Dual

scholarly journals Nonlinearly constrained optimal control problems

1992 ◽  
Vol 33 (4) ◽  
pp. 517-530 ◽  
Author(s):  
K. L. Teo ◽  
K. H. Wong
Keyword(s):  
Optimal Control ◽  
General Class ◽  
State Constraints ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
Continuous State ◽  
Constraint Transcription ◽  
Inequality Type

AbstractIn a paper by Teo and Jennings, a constraint transcription is used together with the concept of control parametrisation to devise a computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type. The aim of this paper is to extend the results to a more general class of constrained optimal control problems, where the problem is also subject to terminal equality state constraints. For illustration, a numerical example is included.

scholarly journals Mesh independence and fast local convergence of a primal-dual active-set method for mixed control-state constrained elliptic control problems

2007 ◽  
Vol 49 (1) ◽  
pp. 1-38 ◽  
Author(s):  
M. Hintermüller
Keyword(s):  
Optimal Control ◽  
Numerical Test ◽  
Control Problems ◽  
Active Set ◽  
Active Set Method ◽  
Constrained Optimal Control ◽  
Mixed Control ◽  
Mesh Independence ◽  
Primal Dual ◽  
Control State

A class of mixed control-state constrained optimal control problems for elliptic partial differential equations arising, for example, in Lavrentiev-type regularized state constrained optimal control is considered. Its numerical solution is obtained via a primal-dual activeset method, which is equivalent to a class of semi-smooth Newton methods. The locally superlinear convergence of the active-set method in function space is established, and its mesh independence is proved. The paper contains a report on numerical test runs including a comparison with a short-step path-following interior-point method and a coarse-to-fine mesh sweep, that is, a nested iteration technique, for accelerating the overall solution process. Finally, convergence and regularity properties of the regularized problems with respect to a vanishing Lavrentiev parameter are considered. 2000 Mathematics subject classification: primary 65K05; secondary 90C33.

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