Computational Comparison of Surface Metrics for PDE Constrained Shape Optimization

Algorithms for PDE-Constrained Optimization

In this paper we review a number of algorithmic approaches for solving optimization problems with PDE constraints. Most of these methods were originally developed for finite dimensional problems. When applied to optimization problems with PDE constraints, new aspects become important. For instance, (discretized) PDE-constrained problems are inherently large-scale. Some aspects, like mesh indepe...

Block-triangular preconditioners for PDE-constrained optimization

Parallel Algorithms for PDE-Constrained Optimization

PDE-constrained optimization refers to the optimization of systems governed by partial differential equations (PDEs). The simulation problem is to solve the PDEs for the state variables (e.g. displacement, velocity, temperature, electric field, magnetic field, species concentration), given appropriate data (e.g. geometry, coefficients, boundary conditions, initial conditions, source functions)....

Interior-Point Methods for PDE-Constrained Optimization

In applied sciences PDEs model an extensive variety of phenomena. Typically the final goal of simulations is a system which is optimal in a certain sense. For instance optimal control problems identify a control to steer a system towards a desired state. Inverse problems seek PDE parameters which are most consistent with measurements. In these optimization problems PDEs appear as equality const...

Constrained Programming for Optimization Problems in PDE

Optimization problems in PDE models are often approached by considering the PDE model as a black-box input-output relation and thus solving an unconstrained optimization problem. In contrast to that, considering the PDE model as a side condition of a resulting constrained programming problem enables us to simultaneously solve the PDE model equations together with the optimization problem. This ...