In this paper a family of trust-region interior-point SQP algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise e.g. from the discretization of optimal control problems. The algorithms treat states and controls as independent variables. They are designed to take advantage of the structure of the problem. In particular they do not rely on matrix factorizations of the linearized constraints, but use solutions of the linearized state equation and the adjoint equation. They are well suited for large scale problems arising from optimal control problems governed by partial differential equations. The algorithms keep strict feasibility with respect to the bound constraints by using an affine scaling method proposed for a different class of problems by Coleman and Li and they exploit trust--region techniques for equality-constrained optimizatio...

this paper we shall use a completely different approach. We determine the unknown nonlinear law directly. Thereby, we restrict ourselves to the linear heat equation and shall use for convenience semigroup methods. In practically meaningful problems the heat equation is nonlinear, too. However, this problem is theoretically much more difficult, as the parabolic initial-boundary value problem does not belong to the class of semilinear systems in this case. We shall formulate an optimal control problem and discuss properties such as existence, uniqueness, stability, wellposedness. Finally, we establish a numerical method to solve this type of problems and numerical results will be presented. For the optimal control theory and the analytical background we refer to R OSCH/TR OLTZSCH [11], where we can find the derivation of the existence of an optimal control, of the necessary first order optimality condition and of the adjoint equation. We are going to investigate the following optimal control problem. The aim consists in minimizing the objective \Phi(ff) =

this paper. For that reason it is convenient to work with different regularization methods, among which the Tikhonov-regularization is the most important, see TIKHONOV/ARSENIN [12], TIKHONOV/GONCHARSKIJ/STEPANOV/YAGOLA [13], MOROZOV [11]. In literature we find two basic different methods to identify boundary conditions. One consists in determining a finite number of parameters. In this approach the solution is supposed to belong to a specified known class of functions. Nonlinear optimization is the basis of this method. For the problem under consideration we refer to KAISER/TR

Abstract. In this paper, we investigate the numerical identification of the diffusion parameters in a linear parabolic problem. The identification is formulated as a constrained minimization problem. By using the augmented Lagrangian method, the inverse problem is reduced to a coupled nonlinear algebraic system, which can be solved efficiently with the preconditioned conjugate gradient method. Finally, we present some numerical experiments to show the efficiency of the proposed methods, even for identifying highly discontinuous parameters. Key Words. Parameter estimation, inverse problems, parabolic equations, augmented Lagrangian methods, conjugate gradient methods. 1.

Consider the heat equation with a nonlinear function ff in the boundary condition which depends only on the solution u of the initial-boundary value problem. The unknown function ff belongs to a set of admissible uniformly Lipschitz continuous functions. For this problem stability estimates of the form kff 1 \Gamma ff 2 k cku 1 \Gamma u 2 k with different norms are derived. Finally an interesting example is discussed. 1 Introduction The identification of coefficients in partial differential equations is a well investigated problem. So we can find many papers especially for the inverse heat conduction problem. In contrast to this, the identification of nonlinear functions is less developed. This also refers to the nonlinear boundary conditions for the heat equation. In many technical processes for instance the cooling of hot steel in fluids the heat exchange coefficient depends on the boundary temperature. For that reason it is necessary to investigate such classes of nonlinear pro...