PDE Constrained Optimization

Characteristics of PDE Constrained Optimization Problems

• All problems are PDE constrained optimization problems - there are many, many more.

• Evaluation of objective function and constraint functions involves expensive simulations (in the previous examples solution of partial differential equations (PDEs)).

• THE optimization problem does not exist. Instead each problem leads to a family of optimization problems which are closely linked. (Hierarchy of optimization problems obtained by refinement of discretization.)

• The robust and efficient solution of such optimization problems requires the integration of application specific structure, numerical simulation and optimization algorithms.