A Trust Region Method for Parabolic Boundary Control Problems
نویسندگان
چکیده
In this paper we develop a trust region algorithm for constrained parabolic boundary control problems. The method is a projected form of the Steihaug trust-region-CG method with a smoothing step added at each iteration to improve performance in the global phase and provide mesh-independent sup-norm convergence in the terminal phase.
منابع مشابه
Implementation of Sinc-Galerkin on Parabolic Inverse problem with unknown boundary condition
The determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. For solving these ill-posed inverse problems, Galerkin method based on Sinc basis functions for space and time will be used. To solve the system of linear equation, a noise is imposed and Tikhonove regularization is applied. By using a sensor located at a point in the domain of $x$, say $...
متن کاملTrust-Region POD using A-Posteriori Error Estimation for Semilinear Parabolic Optimal Control Problems
An optimal control problem governed by a semilinear heat equation is solved using a globalized inexact Newton method. To reduce the computational effort a model order reduction approach based on proper orthogonal decomposition (POD) is applied. Within a trust region framework we guarantee that the reducedorder models are sufficiently accurate by ensuring gradient accuracy. The gradient error is...
متن کاملOn Efficiency of Non-Monotone Adaptive Trust Region and Scaled Trust Region Methods in Solving Nonlinear Systems of Equations
In this paper we run two important methods for solving some well-known problems and make a comparison on their performance and efficiency in solving nonlinear systems of equations. One of these methods is a non-monotone adaptive trust region strategy and another one is a scaled trust region approach. Each of methods showed fast convergence in special problems and slow convergence in other o...
متن کاملOn the Optimal Control of the Free Boundary Problems for the Second Order Parabolic Equations. I. Well-posedness and Convergence of the Method of Lines
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework, where boundary heat flux and free boundary are components of the control vector, and optimality criteria consists of the minimization of the sum of L2-norm ...
متن کاملA MIXED PARABOLIC WITH A NON-LOCAL AND GLOBAL LINEAR CONDITIONS
Krein [1] mentioned that for each PD equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary conditions. They claim it is not possible to have a related boundary value problem for an arbitrarily chosen operator in between. They have only considered lo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM Journal on Optimization
دوره 9 شماره
صفحات -
تاریخ انتشار 1999