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TrustRegion InteriorPoint SQP Algorithms For A Class Of Nonlinear Programming Problems
 SIAM J. CONTROL OPTIM
, 1997
"... In this paper a family of trustregion interiorpoint 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 co ..."
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Cited by 38 (8 self)
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In this paper a family of trustregion interiorpoint 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 trustregion techniques for equalityconstrained optimizatio...
Identification of Nonlinear Heat Transfer Laws By Optimal Control
 Num. Funct. Analysis and Optimization
, 1994
"... 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 ..."
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Cited by 6 (3 self)
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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 initialboundary 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) =
An Optimal Control Problem Arising From the Identification of Nonlinear Heat Transfer Laws
 Archives of Control Sciences
, 1992
"... this paper. For that reason it is convenient to work with different regularization methods, among which the Tikhonovregularization 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 ..."
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Cited by 5 (4 self)
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this paper. For that reason it is convenient to work with different regularization methods, among which the Tikhonovregularization 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
Stability Estimates for the Identification of Nonlinear Heat Transfer Laws
, 1996
"... Consider the heat equation with a nonlinear function ff in the boundary condition which depends only on the solution u of the initialboundary value problem. The unknown function ff belongs to a set of admissible uniformly Lipschitz continuous functions. For this problem stability estimates of the f ..."
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Cited by 3 (1 self)
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Consider the heat equation with a nonlinear function ff in the boundary condition which depends only on the solution u of the initialboundary 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...
Parameter estimation with the augmented Lagrangian method for a parabolic equation
 J. OPTIM. THEORY APPL
, 2005
"... 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 sys ..."
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Cited by 3 (1 self)
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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.
IDENTIFICATION OF DIFFUSION PARAMETERS IN A NONLINEAR CONVECTION–DIFFUSION EQUATION USING THE AUGMENTED LAGRANGIAN METHOD
"... Abstract. Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential equation arises as the saturation equation in the fractional flow formulation of the two–phase porous media flow equations. The forward problem is discretized ..."
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Abstract. Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential equation arises as the saturation equation in the fractional flow formulation of the two–phase porous media flow equations. The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained minimization problem. We utilize the augmented Lagrangian method and transform the minimization problem into a coupled system of nonlinear algebraic equations, which is solved efficiently with the nonlinear conjugate gradient method. Numerical experiments are presented and discussed. 1.
SOME REMARKS ON AUGMENTED LAGRANGENEWTON SQP METHODS
"... Abstract. An augmented LagrangianSQP algorithm for optimal control of differential equations in Hilbert spaces is analyzed. This algorithm has secondorder convergence rate provided that a secondorder sufficient optimality condition is satisfied. 1. ..."
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Abstract. An augmented LagrangianSQP algorithm for optimal control of differential equations in Hilbert spaces is analyzed. This algorithm has secondorder convergence rate provided that a secondorder sufficient optimality condition is satisfied. 1.
© 2003 Kluwer Academic Publishers. Printed in the Netherlands. On a Fourier method of embedding domains using an optimal distributed control
, 2001
"... We propose a domain embedding method to solve second order elliptic problems in arbitrary twodimensional domains. This method can be easily extended to threedimensional problems. The method is based on formulating the problem as an optimal distributed control problem inside a rectangle in which th ..."
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We propose a domain embedding method to solve second order elliptic problems in arbitrary twodimensional domains. This method can be easily extended to threedimensional problems. The method is based on formulating the problem as an optimal distributed control problem inside a rectangle in which the arbitrary domain is embedded. A periodic solution of the equation under consideration is constructed easily by making use of Fourier series. Numerical results obtained for Dirichlet problems are presented. The numerical tests show a high accuracy of the proposed algorithm and the computed solutions are in very good agreement with the exact solutions.