Multiobjective PDE-constrained optimization using the reduced-basis method

In this paper the reduced basis method is utilized to solve multiobjective optimization problems governed by linear variational equations. These problems often arise in practical applications, where the quality of the system behavior has to be measured by more than one criterium. For the numerical solution the weighting sum method is applied. This approach leads to an algorithm, where many parameterized quadratic optimization problems are solved very efficiently by a appropriate reduced basis approximation. Further, the number of parameter variations is reduced by a sensitivity analysis for the parameterized objective.