## Optimal Control of Partial Differential Equations: Proceedings of the IFIP WG 7.2 International Conference, Irsee, April 9-12, 1990The purpose of the Conference on Optimal Control of Partial Differential Equations was to bring together leading experts in this field and to exchange ideas and information about recent advances in control theory connected with partial differential equations. The papers collected in these Proceedings are mainly research papers in which new results are presented. Out of a broad spectrum of topics the problem of exact controllability played a central role, and also shape control was given some special attention. Nonlinear problems were mainly treated under the aspect of optimality whereas identification problems and also numerical aspects were considered only treated marginally. |

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adjoint Algorithm application approximation assume assumptions Banach space BFGS Method boundary conditions boundary value problem bounded Compute cone consider continuous continuous embeddings control systems convergence convex convex cone corresponding curl defined denotes derivative dimensional Dirichlet discrete distributed parameter systems domain dual dual space dx dt element elliptic estimates exists a constant finite energy finite-dimensional Fourier given Hence Hessian Hilbert space hypotheses inequality isomorphism iteration Lasiecka Lemma linear Lipschitz Lipschitz continuous Math matrix Minimize Moreover nodes nonlinear norm obtain operator optimal control problems optimal problem optimality conditions partial differential equations perturbations positive definite Proof properties prove quasi-Newton methods reachable set reduced SQP method regularity Remark resp respect result satisfies second order semigroup sequence Shape gradient Shape Hessian solve stability subset Suppose surjective Theorem 2.1 theory topology transformations unique solution variation vector velocity fields verified wave equation weak Zolesio