Author:
Bernreuther Marco,Müller Georg,Volkwein Stefan
Abstract
AbstractThis work deals with the efficient numerical characterization of Pareto stationary fronts for multiobjective optimal control problems with a moderate number of cost functionals and a mildly nonsmooth, elliptic, semilinear PDE-constraint. When “ample” controls are considered, strong stationarity conditions that can be used to numerically characterize the Pareto stationary fronts are known for our problem. We show that for finite dimensional controls, a sufficient adjoint-based stationarity system remains obtainable. It turns out that these stationarity conditions remain useful when numerically characterizing the fronts, because they correspond to strong stationarity systems for problems obtained by application of weighted-sum and reference point techniques to the multiobjective problem. We compare the performance of both scalarization techniques using quantifiable measures for the approximation quality. The subproblems of either method are solved with a line-search globalized pseudo-semismooth Newton method that appears to remove the degenerate behavior of the local version of the method employed previously. We apply a matrix-free, iterative approach to deal with the memory and complexity requirements when solving the subproblems of the reference point method and compare several preconditioning approaches.
Funder
Deutsche Forschungsgemeinschaft
Universität Konstanz
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Control and Optimization
Reference21 articles.
1. Alnaes, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., Wells, G.N.: The fenics project version 1.5. Arch. Numer. Softw. 3(100), 9–23. https://doi.org/10.11588/ans.2015.100.20553
2. Banholzer, S.: POD-based bicriterial optimal control of convection-diffusion equations. Master’s thesis, Universität, Konstanz (2017)
3. Banholzer, S.: ROM-based multiobjective optimization with PDE constraints. Ph.D. thesis, Universität Konstanz, Konstanz (2021)
4. Banholzer, S., Volkwein, S.: Hierarchical convex multiobjective optimization by the Euclidean reference point method (2019)
5. Bernreuther, M., Müller, G., Volkwein, S.: 1 reduced basis model order reduction in optimal control of a nonsmooth semilinear elliptic PDE. In: Optimization and Control for Partial Differential Equations, pp. 1–32. De Gruyter (2022)
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