Gradient-Based Multiobjective Optimization with Uncertainties

S. Peitz, M. Dellnitz, in: NEO 2016, Cham, 2017, pp. 159–182.

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Conference Paper | Published | English
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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.
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NEO 2016
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159-182
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Peitz S, Dellnitz M. Gradient-Based Multiobjective Optimization with Uncertainties. In: NEO 2016. Cham; 2017:159-182. doi:10.1007/978-3-319-64063-1_7
Peitz, S., & Dellnitz, M. (2017). Gradient-Based Multiobjective Optimization with Uncertainties. In NEO 2016 (pp. 159–182). Cham. https://doi.org/10.1007/978-3-319-64063-1_7
@inproceedings{Peitz_Dellnitz_2017, place={Cham}, title={Gradient-Based Multiobjective Optimization with Uncertainties}, DOI={10.1007/978-3-319-64063-1_7}, booktitle={NEO 2016}, author={Peitz, Sebastian and Dellnitz, Michael}, year={2017}, pages={159–182} }
Peitz, Sebastian, and Michael Dellnitz. “Gradient-Based Multiobjective Optimization with Uncertainties.” In NEO 2016, 159–82. Cham, 2017. https://doi.org/10.1007/978-3-319-64063-1_7.
S. Peitz and M. Dellnitz, “Gradient-Based Multiobjective Optimization with Uncertainties,” in NEO 2016, 2017, pp. 159–182.
Peitz, Sebastian, and Michael Dellnitz. “Gradient-Based Multiobjective Optimization with Uncertainties.” NEO 2016, 2017, pp. 159–82, doi:10.1007/978-3-319-64063-1_7.

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