A domain decomposition method for optimization problems for partial differential equations

A nonoverlapping domain decomposition method for optimization problems for partial differential equations is presented. The domain decomposition is ef fected through an auxiliary optimization problem. This results in an multio bjective optimization problem involving the given Functional and the auxili ary functional. The existence of an optimal solution to the multiobjective optimization problem is proved as are convergence estimates as the paramete rs used to regularize the problem (penalty parameters) and to combine the t wo objective functionals tend to zero.;in optimality system for the optimal solution is derived and used to define a gradient method. Convergence resu lts are obtained for the gradient method and the results of some numerical experiments are obtained. Then, unregularized problems having vanishing pen alty parameters are discussed. (C) 2000 Elsevier Science Ltd. All rights re served.