An optimal control problem governed by a bilinear elliptic equation is considered. This problem is solved by the sequential quadratic programming (SQP) method in an infinite-dimensional framework. In each level of this iterative method the solution of linear-quadratic subproblem is computed by a Galerkin projection using proper orthogonal decomposition (POD). Thus, an approximate (inexact) solution of the subproblem is determined. Based on a POD error estimator developed by Tröltzsch and Volkwein...
Proper orthogonal decomposition (POD) is a powerful technique for model reduction of linear and non-linear systems. It is based on a Galerkin type discretization with basis elements created from the system itself. In this work, error estimates for Galerkin POD methods for linear elliptic, parameter-dependent systems are proved. The resulting error bounds depend on the number of POD basis functions and on the parameter grid that is used to generate the snapshots and to compute the POD basis. The...
An optimal control problem governed by a bilinear elliptic equation is considered. This
problem is solved by the sequential quadratic programming (SQP) method in an
infinite-dimensional framework. In each level of this iterative method the solution of
linear-quadratic subproblem is computed by a Galerkin projection using proper orthogonal
decomposition (POD). Thus, an approximate (inexact) solution of the subproblem is
determined. Based on a POD...
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