### Abstract

A nonoverlapping domain decomposition method for optimization problems for partial differential equations is presented. The domain decomposition is effected through an auxiliary optimization problem. This results in an multiobjective optimization problem involving the given functional and the auxiliary functional. The existence of an optimal solution to the multiobjective optimization problem is proved as are convergence estimates as the parameters used to regularize the problem (penalty parameters) and to combine the two objective functionals tend to zero. An optimality system for the optimal solution is derived and used to define a gradient method. Convergence results are obtained for the gradient method and the results of some numerical experiments are obtained. Then, unregularized problems having vanishing penalty parameters are discussed.

Original language | English |
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Pages (from-to) | 177-192 |

Number of pages | 16 |

Journal | Computers and Mathematics with Applications |

Volume | 40 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2000 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

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*Computers and Mathematics with Applications*, vol. 40, no. 2, pp. 177-192. https://doi.org/10.1016/S0898-1221(00)00152-8

**Domain decomposition method for optimization problems for partial differential equations.** / Gunzburger, M. D.; Lee, Jeehyun.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Domain decomposition method for optimization problems for partial differential equations

AU - Gunzburger, M. D.

AU - Lee, Jeehyun

PY - 2000/1/1

Y1 - 2000/1/1

N2 - A nonoverlapping domain decomposition method for optimization problems for partial differential equations is presented. The domain decomposition is effected through an auxiliary optimization problem. This results in an multiobjective optimization problem involving the given functional and the auxiliary functional. The existence of an optimal solution to the multiobjective optimization problem is proved as are convergence estimates as the parameters used to regularize the problem (penalty parameters) and to combine the two objective functionals tend to zero. An optimality system for the optimal solution is derived and used to define a gradient method. Convergence results are obtained for the gradient method and the results of some numerical experiments are obtained. Then, unregularized problems having vanishing penalty parameters are discussed.

AB - A nonoverlapping domain decomposition method for optimization problems for partial differential equations is presented. The domain decomposition is effected through an auxiliary optimization problem. This results in an multiobjective optimization problem involving the given functional and the auxiliary functional. The existence of an optimal solution to the multiobjective optimization problem is proved as are convergence estimates as the parameters used to regularize the problem (penalty parameters) and to combine the two objective functionals tend to zero. An optimality system for the optimal solution is derived and used to define a gradient method. Convergence results are obtained for the gradient method and the results of some numerical experiments are obtained. Then, unregularized problems having vanishing penalty parameters are discussed.

UR - http://www.scopus.com/inward/record.url?scp=0034230430&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034230430&partnerID=8YFLogxK

U2 - 10.1016/S0898-1221(00)00152-8

DO - 10.1016/S0898-1221(00)00152-8

M3 - Article

VL - 40

SP - 177

EP - 192

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 2

ER -