POD-based error control for reduced-order bicriterial PDE-constrained optimization

POD-based error control for reduced-order bicriterial PDE-constrained optimization

In the present paper, a bicriterial optimal control problem governed by an abstract evolution problem and bilateral control constraints is considered. To compute Pareto optimal points and the Pareto front numerically, the (Euclidean) reference point method is applied, where many scalar constrained optimization problems have to be solved. For this reason a reduced-order approach based on proper ...

Lossy compression for PDE-constrained optimization: adaptive error control

For the solution of optimal control problems governed by nonlinear parabolic PDEs, methods working on the reduced objective functional are often employed to avoid a full spatio-temporal discretization of the problem. The evaluation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint e...

Reduced-Order Galerkin Approximations in PDE Constrained Optimization

Efficient POD reduced-order modeling for parametrized nonlinear PDE systems

In this paper a model order reduction method for a nonlinear elliptic-parabolic system is developed. Systems of this type arise from mathematical models for lithium ion batteries. A non-intrusive reduced order approach based on proper orthogonal decomposition (POD) is presented. In addition to this the interpolation method introduced by Barrault et al. [3] is applied in order to achieve efficie...

Model Order Reduction for PDE Constrained Optimization

The optimization and control of systems governed by partial differential equations (PDEs) usually requires numerous evaluations of the forward problem or the optimality system. Despite the fact that many recent efforts, many of which are reported in this book, have been made to limit or reduce the number of evaluations to 5–10, this cannot be achieved in all situations and even if this is possi...