In this study, we apply a domain decomposition algorithm based on optimization technique to optimal control problems governed by an elliptic partial differential equation with random inputs. The domain decomposition is implemented by introducing an auxiliary optimal control problem, which results in a multi-objective optimization problem. We prove the existence of a solution to the resulting optimization problem as well as the convergence to the optimal solution of original control problem. Solutions of the domain decomposition problem are determined from an optimality system and error estimates for finite element approximations are analyzed. Finally, some numerical experiments are provided to confirm theoretical results.
Bibliographical noteFunding Information:
The work of Jeehyun Lee was supported by Mid-Career Research Program (NRF-2015R1A5A1009350) and Science Research Center (NRF-2016R1A2B4014178) through the National Research Foundation of Korea.
© 2019 Elsevier Inc.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics