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

Yoongu Hwang; Jangwoon Lee; Jeehyun Lee; Myoungho Yoon

doi:10.1016/j.amc.2019.124674

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

Yoongu Hwang, Jangwoon Lee, Jeehyun Lee, Myoungho Yoon

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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
Article number	124674
Journal	Applied Mathematics and Computation
Volume	364
DOIs	https://doi.org/10.1016/j.amc.2019.124674
Publication status	Published - 2020 Jan 1

Bibliographical note

Funding 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.

Publisher Copyright:
© 2019 Elsevier Inc.

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2019.124674

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title = "A domain decomposition algorithm for optimal control problems governed by elliptic PDEs with random inputs",

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.",

author = "Yoongu Hwang and Jangwoon Lee and Jeehyun Lee and Myoungho Yoon",

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AU - Hwang, Yoongu

AU - Lee, Jangwoon

AU - Lee, Jeehyun

AU - Yoon, Myoungho

N1 - Funding 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. Publisher Copyright: © 2019 Elsevier Inc.

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.

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

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