Lectures Notes Algorithms and Preconditioning in PDE-Constrained Optimization
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A preconditioning technique for a class of PDE-constrained optimization problems
We investigate the use of a preconditioning technique for solving linear systems of saddle point type arising from the application of an inexact Gauss–Newton scheme to PDE-constrained optimization problems with a hyperbolic constraint. The preconditioner is of block triangular form and involves diagonal perturbations of the (approximate) Hessian to insure nonsingularity and an approximate Schur...
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The presented approach aims at solving an equality constrained, finite-dimensional optimization problem, where the constraints arise from the discretization of some partial differential equation (PDE) on a given space grid. For this purpose, a stationary point of the Lagrangian is computed using Newton’s method, which requires the repeated solution of KKT systems. The proposed algorithm focuses...
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تاریخ انتشار 2012