| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 59 | |
| Number of page(s) | 38 | |
| DOI | https://doi.org/10.1051/cocv/2024049 | |
| Published online | 28 August 2024 | |
Interior point methods in optimal control
IFP Energies nouvelles, Applied Mathematics Department, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France
* Corresponding author: paul.malisani@ifpen.fr
Received:
25
April
2023
Accepted:
14
June
2024
This paper deals with Interior Point Methods (IPMs) for Optimal Control Problems (OCPs) with pure state and mixed constraints. This paper establishes a complete proof of convergence of IPMs for a general class of OCPs. Convergence results are proved for primal variables, namely state and control variables, and for dual variables, namely, the adjoint state, and the constraints multipliers. In addition, the presented convergence result does not rely on a strong convexity assumption. Finally, this paper compares the performances of a primal and a primal-dual implementation of IPMs in optimal control in three examples.
Mathematics Subject Classification: 49K15 / 49M05 / 49M29
Key words: Optimal control / state constraints / mixed constraints / interior point methods / primal-dual methods
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.