### Abstract

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.

Original language | English |
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Article number | 124674 |

Journal | Applied Mathematics and Computation |

Volume | 364 |

DOIs | |

Publication status | Published - 2020 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Computational Mathematics
- Applied Mathematics

### Cite this

*Applied Mathematics and Computation*,

*364*, [124674]. https://doi.org/10.1016/j.amc.2019.124674

}

*Applied Mathematics and Computation*, vol. 364, 124674. https://doi.org/10.1016/j.amc.2019.124674

**A domain decomposition algorithm for optimal control problems governed by elliptic PDEs with random inputs.** / Hwang, Yoongu; Lee, Jangwoon; Lee, Jeehyun; Yoon, Myoungho.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A domain decomposition algorithm for optimal control problems governed by elliptic PDEs with random inputs

AU - Hwang, Yoongu

AU - Lee, Jangwoon

AU - Lee, Jeehyun

AU - Yoon, Myoungho

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85071583907&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071583907&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2019.124674

DO - 10.1016/j.amc.2019.124674

M3 - Article

AN - SCOPUS:85071583907

VL - 364

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

M1 - 124674

ER -