An efficient descent method for locally Lipschitz multiobjective optimization problems
B. Gebken, S. Peitz, Journal of Optimization Theory and Applications (2021).
Journal Article
| English
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Abstract
In this article, we present an efficient descent method for locally Lipschitz
continuous multiobjective optimization problems (MOPs). The method is realized
by combining a theoretical result regarding the computation of descent
directions for nonsmooth MOPs with a practical method to approximate the
subdifferentials of the objective functions. We show convergence to points
which satisfy a necessary condition for Pareto optimality. Using a set of test
problems, we compare our method to the multiobjective proximal bundle method by
M\"akel\"a. The results indicate that our method is competitive while being
easier to implement. While the number of objective function evaluations is
larger, the overall number of subgradient evaluations is lower. Finally, we
show that our method can be combined with a subdivision algorithm to compute
entire Pareto sets of nonsmooth MOPs.
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Journal Title
Journal of Optimization Theory and Applications
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Cite this
Gebken B, Peitz S. An efficient descent method for locally Lipschitz multiobjective optimization problems. Journal of Optimization Theory and Applications. 2021. doi:10.1007/s10957-020-01803-w
Gebken, B., & Peitz, S. (2021). An efficient descent method for locally Lipschitz multiobjective optimization problems. Journal of Optimization Theory and Applications. https://doi.org/10.1007/s10957-020-01803-w
@article{Gebken_Peitz_2021, title={An efficient descent method for locally Lipschitz multiobjective optimization problems}, DOI={10.1007/s10957-020-01803-w}, journal={Journal of Optimization Theory and Applications}, author={Gebken, Bennet and Peitz, Sebastian}, year={2021} }
Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” Journal of Optimization Theory and Applications, 2021. https://doi.org/10.1007/s10957-020-01803-w.
B. Gebken and S. Peitz, “An efficient descent method for locally Lipschitz multiobjective optimization problems,” Journal of Optimization Theory and Applications, 2021.
Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems.” Journal of Optimization Theory and Applications, 2021, doi:10.1007/s10957-020-01803-w.
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