✦ LIBER ✦

A domain decomposition method for optimization problems for partial differential equations

✍ Scribed by M.D. Gunzburger; Jeehyun Lee

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 786 KB
Volume: 40
Category: Article
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(00)00152-8

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✦ Synopsis

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. (~ 2000 Elsevier Science Ltd. All rights reserved. Keywords--Optimization problems for partial differential equations, Nonoverlapping domain decomposition methods, Multiobjective optimization.

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