[{"publication_status":"published","publication_identifier":{"issn":["1860-949X","1860-9503"],"isbn":["9783319961033","9783319961040"]},"place":"Cham","year":"2018","citation":{"apa":"Gebken, B., Peitz, S., &#38; Dellnitz, M. (2018). A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems. In <i>Numerical and Evolutionary Optimization – NEO 2017</i>. Cham. <a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">https://doi.org/10.1007/978-3-319-96104-0_2</a>","short":"B. Gebken, S. Peitz, M. Dellnitz, in: Numerical and Evolutionary Optimization – NEO 2017, Cham, 2018.","bibtex":"@inproceedings{Gebken_Peitz_Dellnitz_2018, place={Cham}, title={A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">10.1007/978-3-319-96104-0_2</a>}, booktitle={Numerical and Evolutionary Optimization – NEO 2017}, author={Gebken, Bennet and Peitz, Sebastian and Dellnitz, Michael}, year={2018} }","mla":"Gebken, Bennet, et al. “A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems.” <i>Numerical and Evolutionary Optimization – NEO 2017</i>, 2018, doi:<a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">10.1007/978-3-319-96104-0_2</a>.","ama":"Gebken B, Peitz S, Dellnitz M. A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems. In: <i>Numerical and Evolutionary Optimization – NEO 2017</i>. Cham; 2018. doi:<a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">10.1007/978-3-319-96104-0_2</a>","ieee":"B. Gebken, S. Peitz, and M. Dellnitz, “A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems,” in <i>Numerical and Evolutionary Optimization – NEO 2017</i>, 2018.","chicago":"Gebken, Bennet, Sebastian Peitz, and Michael Dellnitz. “A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems.” In <i>Numerical and Evolutionary Optimization – NEO 2017</i>. Cham, 2018. <a href=\"https://doi.org/10.1007/978-3-319-96104-0_2\">https://doi.org/10.1007/978-3-319-96104-0_2</a>."},"date_updated":"2022-01-06T07:04:00Z","date_created":"2019-03-29T13:26:47Z","author":[{"last_name":"Gebken","full_name":"Gebken, Bennet","id":"32643","first_name":"Bennet"},{"first_name":"Sebastian","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X","full_name":"Peitz, Sebastian","id":"47427"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"title":"A Descent Method for Equality and Inequality Constrained Multiobjective Optimization Problems","doi":"10.1007/978-3-319-96104-0_2","conference":{"name":"NEO 2017: Numerical and Evolutionary Optimization"},"type":"conference","publication":"Numerical and Evolutionary Optimization – NEO 2017","abstract":[{"text":"In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained problems by using two active set strategies. Under some regularity assumptions on the problem, we show that accumulation points of our descent method satisfy a necessary condition for local Pareto optimality. Finally, we show the typical behavior of our method in a numerical example.","lang":"eng"}],"status":"public","_id":"8750","user_id":"47427","department":[{"_id":"101"}],"language":[{"iso":"eng"}]},{"author":[{"first_name":"Sebastian","full_name":"Peitz, Sebastian","id":"47427","last_name":"Peitz","orcid":"https://orcid.org/0000-0002-3389-793X"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"}],"date_created":"2019-03-29T13:28:56Z","date_updated":"2022-01-06T07:04:00Z","doi":"10.1007/978-3-319-64063-1_7","title":"Gradient-Based Multiobjective Optimization with Uncertainties","publication_status":"published","publication_identifier":{"isbn":["9783319640624","9783319640631"],"issn":["1860-949X","1860-9503"]},"citation":{"apa":"Peitz, S., &#38; Dellnitz, M. (2017). Gradient-Based Multiobjective Optimization with Uncertainties. In <i>NEO 2016</i> (pp. 159–182). Cham. <a href=\"https://doi.org/10.1007/978-3-319-64063-1_7\">https://doi.org/10.1007/978-3-319-64063-1_7</a>","mla":"Peitz, Sebastian, and Michael Dellnitz. “Gradient-Based Multiobjective Optimization with Uncertainties.” <i>NEO 2016</i>, 2017, pp. 159–82, doi:<a href=\"https://doi.org/10.1007/978-3-319-64063-1_7\">10.1007/978-3-319-64063-1_7</a>.","bibtex":"@inproceedings{Peitz_Dellnitz_2017, place={Cham}, title={Gradient-Based Multiobjective Optimization with Uncertainties}, DOI={<a href=\"https://doi.org/10.1007/978-3-319-64063-1_7\">10.1007/978-3-319-64063-1_7</a>}, booktitle={NEO 2016}, author={Peitz, Sebastian and Dellnitz, Michael}, year={2017}, pages={159–182} }","short":"S. Peitz, M. Dellnitz, in: NEO 2016, Cham, 2017, pp. 159–182.","ieee":"S. Peitz and M. Dellnitz, “Gradient-Based Multiobjective Optimization with Uncertainties,” in <i>NEO 2016</i>, 2017, pp. 159–182.","chicago":"Peitz, Sebastian, and Michael Dellnitz. “Gradient-Based Multiobjective Optimization with Uncertainties.” In <i>NEO 2016</i>, 159–82. Cham, 2017. <a href=\"https://doi.org/10.1007/978-3-319-64063-1_7\">https://doi.org/10.1007/978-3-319-64063-1_7</a>.","ama":"Peitz S, Dellnitz M. Gradient-Based Multiobjective Optimization with Uncertainties. In: <i>NEO 2016</i>. Cham; 2017:159-182. doi:<a href=\"https://doi.org/10.1007/978-3-319-64063-1_7\">10.1007/978-3-319-64063-1_7</a>"},"page":"159-182","place":"Cham","year":"2017","user_id":"47427","department":[{"_id":"101"}],"project":[{"name":"Computing Resources Provided by the Paderborn Center for Parallel Computing","_id":"52"}],"_id":"8752","language":[{"iso":"eng"}],"type":"conference","publication":"NEO 2016","status":"public","abstract":[{"lang":"eng","text":"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."}]},{"status":"public","type":"book_chapter","publication":"EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation","language":[{"iso":"eng"}],"_id":"16670","user_id":"15701","department":[{"_id":"101"}],"year":"2013","place":"Berlin, Heidelberg","citation":{"ama":"Schütze O, Witting K, Ober-Blöbaum S, Dellnitz M. Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems. In: <i>EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation</i>. Berlin, Heidelberg; 2013. doi:<a href=\"https://doi.org/10.1007/978-3-642-32726-1_5\">10.1007/978-3-642-32726-1_5</a>","chicago":"Schütze, Oliver, Katrin Witting, Sina Ober-Blöbaum, and Michael Dellnitz. “Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems.” In <i>EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation</i>. Berlin, Heidelberg, 2013. <a href=\"https://doi.org/10.1007/978-3-642-32726-1_5\">https://doi.org/10.1007/978-3-642-32726-1_5</a>.","ieee":"O. Schütze, K. Witting, S. Ober-Blöbaum, and M. Dellnitz, “Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems,” in <i>EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation</i>, Berlin, Heidelberg, 2013.","apa":"Schütze, O., Witting, K., Ober-Blöbaum, S., &#38; Dellnitz, M. (2013). Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems. In <i>EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation</i>. Berlin, Heidelberg. <a href=\"https://doi.org/10.1007/978-3-642-32726-1_5\">https://doi.org/10.1007/978-3-642-32726-1_5</a>","bibtex":"@inbook{Schütze_Witting_Ober-Blöbaum_Dellnitz_2013, place={Berlin, Heidelberg}, title={Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems}, DOI={<a href=\"https://doi.org/10.1007/978-3-642-32726-1_5\">10.1007/978-3-642-32726-1_5</a>}, booktitle={EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation}, author={Schütze, Oliver and Witting, Katrin and Ober-Blöbaum, Sina and Dellnitz, Michael}, year={2013} }","mla":"Schütze, Oliver, et al. “Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems.” <i>EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation</i>, 2013, doi:<a href=\"https://doi.org/10.1007/978-3-642-32726-1_5\">10.1007/978-3-642-32726-1_5</a>.","short":"O. Schütze, K. Witting, S. Ober-Blöbaum, M. Dellnitz, in: EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation, Berlin, Heidelberg, 2013."},"publication_status":"published","publication_identifier":{"isbn":["9783642327254","9783642327261"],"issn":["1860-949X","1860-9503"]},"title":"Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems","doi":"10.1007/978-3-642-32726-1_5","date_updated":"2022-01-06T06:52:54Z","author":[{"full_name":"Schütze, Oliver","last_name":"Schütze","first_name":"Oliver"},{"first_name":"Katrin","full_name":"Witting, Katrin","last_name":"Witting"},{"full_name":"Ober-Blöbaum, Sina","last_name":"Ober-Blöbaum","first_name":"Sina"},{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"}],"date_created":"2020-04-16T10:05:59Z"}]