Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/307013 
Year of Publication: 
2022
Citation: 
[Journal:] Computational Optimization and Applications [ISSN:] 1573-2894 [Volume:] 83 [Issue:] 2 [Publisher:] Springer US [Place:] New York, NY [Year:] 2022 [Pages:] 435-464
Publisher: 
Springer US, New York, NY
Abstract: 
This 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.
Subjects: 
Multiobjective optimal control
Nonsmooth optimization
Stationarity conditions
Pareto optimality
Scalarization methods
Pseudo-semismooth Newton method
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version

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