ROM-Based Inexact Subdivision Methods for PDE-Constrained Multiobjective Optimization

Adaptive Multilevel Inexact SQP Methods for PDE-Constrained Optimization

We present a class of inexact adaptive multilevel trust-region SQP-methods for the efficient solution of optimization problems governed by nonlinear partial differential equations. The algorithm starts with a coarse discretization of the underlying optimization problem and provides during the optimization process 1) implementable criteria for an adaptive refinement strategy of the current discr...

Quasi-Newton Methods for Nonconvex Constrained Multiobjective Optimization

Here, a quasi-Newton algorithm for constrained multiobjective optimization is proposed. Under suitable assumptions, global convergence of the algorithm is established.

Inexact Interior-Point Method for PDE-Constrained Nonlinear Optimization

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...

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 para...