Efficient scalarization in multiobjective optimal control of a nonsmooth PDE

Abstract This work deals with the efficient numerical characterization of Pareto stationary fronts for multiobjective optimal control problems a moderate number cost functionals and mildly nonsmooth, elliptic, semilinear PDE-constraint. When “ample” controls are considered, strong stationarity conditions that can be used to numerically characterize known our problem. We show finite dimensional controls, sufficient adjoint-based system remains obtainable. It turns out these remain useful when characterizing fronts, because they correspond systems obtained by application weighted-sum reference point techniques compare performance both scalarization using quantifiable measures approximation quality. The subproblems either method solved line-search globalized pseudo-semismooth Newton appears remove degenerate behavior local version employed previously. apply matrix-free, iterative approach deal memory complexity requirements solving several preconditioning approaches.