On the Uniform Convergence Analysis of the Schwarz Alternating Method for Optimal Control Problems

Keywords

Advanced Numerical Methods for Scientific Computing
Code:
62/2026
Title:
On the Uniform Convergence Analysis of the Schwarz Alternating Method for Optimal Control Problems
Date:
Wednesday 1st July 2026
Author(s):
Ciaramella, G.; Gong, W.; Kwok, F.; Tan, Z.
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Abstract:
In this paper, we investigate the uniform convergence of the Schwarz alternating method for unconstrained elliptic optimal control problems in one dimension. We derive the convergence factor of the method and find that the convergence factor of the method can be uniformly bounded by a factor ($<1$) associated with that for the state equation. We also observe that the local error propagation operators of the method under a standard choice of energy norms in the robust analysis of optimal control problems are nonexpansive. These observations indicate that the existing convergence analysis frameworks of domain decomposition methods for PDEs based on the standard choice of energy norms are not straightforwardly applicable to that for optimal control problems.
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Proceeding of the 29th International Conference on Domain Decomposition Methods.