Publikation: ROM-based inexact subdivision methods for PDE-constrained multiobjective optimization
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Zusammenfassung
The goal in multiobjective optimization is to determine the so-called Pareto set. Our optimization problem is governed by a parameter dependent semilinear elliptic partial differential equation (PDE). To solve it, we use a gradient based set-oriented numerical method. The numerical solution of the PDE by standard discretization methods usually leads to high computational effort. To overcome this difficulty, reduced-order modeling (ROM) is developed utilizing the reduced basis method. These model simplifications cause inexactness in the gradients. For that reason, an additional descent condition is proposed. Applying a modified subdivision algorithm, numerical experiments illustrate the efficiency of our solution approach.