| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 22 | |
| Number of page(s) | 26 | |
| DOI | https://doi.org/10.1051/cocv/2024003 | |
| Published online | 04 April 2024 | |
Lagrangian dual method for solving stochastic linear quadratic optimal control problems with terminal state constraints
1
School of Mathematical Sciences, Sichuan Normal University,
Chengdu
610066,
PR China
2
School of Mathematics, Sichuan University,
Chengdu
610068,
PR China
* Corresponding author: haisenzhang@yeah.net
Received:
18
January
2023
Accepted:
8
January
2024
A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost functional and a surjectivity condition on the linear constraint mapping. Based on the Lagrangian duality, two approaches are proposed to solve the constrained stochastic LQ problem. First, a theoretical method is given to construct the closed-form solution by the strong duality. Second, an iterative algorithm, called augmented Lagrangian method (ALM), is proposed. The strong convergence of the iterative sequence generated by ALM is proved. In addition, some sufficient conditions for the surjectivity of the linear constraint mapping are obtained.
Mathematics Subject Classification: 93E20 / 49N10 / 49N15 / 49M37
Key words: Stochastic linear quadratic optimal control problem / Lagrangian duality / Riccati equation / augmented Lagrangian method / rank condition
© 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.