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NEO 2016 pp 159-182 | Cite as

Gradient-Based Multiobjective Optimization with Uncertainties

  • Sebastian PeitzEmail author
  • Michael Dellnitz
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 731)

Abstract

In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for inaccuracies in the gradients and then incorporated into a subdivision algorithm for the computation of global solutions to multiobjective optimization problems. Convergence to a superset of the Pareto set is proved and an upper bound for the maximal distance to the set of substationary points is given. Besides the applicability to problems with uncertainties, the algorithm is developed with the intention to use it in combination with model order reduction techniques in order to efficiently solve PDE-constrained multiobjective optimization problems.

Notes

Acknowledgements

This work is supported by the Priority Programme SPP 1962 “Non-smooth and Complementarity-based Distributed Parameter Systems” of the German Research Foundation (DFG).

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsPaderborn UniversityPaderbornGermany

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