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In the present paper non-convex multi-objective parameter optimizationproblems are considered which are governed by elliptic parametrized partialdifferential equations (PDEs). To solve these problems numerically thePascoletti-Serafini scalarization is applied and the obtained scalaroptimization problems are solved by an augmented Lagrangian method. However,due to the PDE constraints, the numerical solution is very expensive so that amodel reduction is utilized by using the reduced basis (RB) method. The qualityof the RB approximation is ensured by a trust-region strategy which does notrequire any offline procedure, where the RB functions are computed in a greedyalgorithm. Moreover, convergence of the proposed method is guaranteed.Numerical examples illustrate the efficiency of the proposed solutiontechnique.

A trust region reduced basis Pascoletti-Serafini algorithm for multi-objective PDE-constrained parameter optimization