[{"place":"Kassel","date_created":"2019-03-25T15:35:23Z","department":[{"_id":"10"}],"type":"conference","citation":{"mla":"Liebendörfer, Michael, and Reinhard Hochmuth. “Perceived Competence and Incompetence in the First Year of Mathematics Studies: Forms and Situations.” <i>Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings</i>, edited by Robin Göller et al., Universität Kassel, 2017, pp. 286–93.","ama":"Liebendörfer M, Hochmuth R. Perceived Competence and Incompetence in the First Year of Mathematics Studies: Forms and Situations. In: Göller R, Biehler R, Hochmuth R, Rück H-G, eds. <i>Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings</i>. Kassel: Universität Kassel; 2017:286-293.","bibtex":"@inproceedings{Liebendörfer_Hochmuth_2017, place={Kassel}, title={Perceived Competence and Incompetence in the First Year of Mathematics Studies: Forms and Situations}, booktitle={Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings}, publisher={Universität Kassel}, author={Liebendörfer, Michael and Hochmuth, Reinhard}, editor={Göller, Robin and Biehler, Rolf and Hochmuth, Reinhard and Rück, Hans-GeorgEditors}, year={2017}, pages={286–293} }","apa":"Liebendörfer, M., &#38; Hochmuth, R. (2017). Perceived Competence and Incompetence in the First Year of Mathematics Studies: Forms and Situations. In R. Göller, R. Biehler, R. Hochmuth, &#38; H.-G. Rück (Eds.), <i>Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings</i> (pp. 286–293). Kassel: Universität Kassel.","ieee":"M. Liebendörfer and R. Hochmuth, “Perceived Competence and Incompetence in the First Year of Mathematics Studies: Forms and Situations,” in <i>Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings</i>, 2017, pp. 286–293.","short":"M. Liebendörfer, R. Hochmuth, in: R. Göller, R. Biehler, R. Hochmuth, H.-G. Rück (Eds.), Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings, Universität Kassel, Kassel, 2017, pp. 286–293.","chicago":"Liebendörfer, Michael, and Reinhard Hochmuth. “Perceived Competence and Incompetence in the First Year of Mathematics Studies: Forms and Situations.” In <i>Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings</i>, edited by Robin Göller, Rolf Biehler, Reinhard Hochmuth, and Hans-Georg Rück, 286–93. Kassel: Universität Kassel, 2017."},"publication":"Didactics of Mathematics in Higher Education as a Scientific Discipline - Conference Proceedings","extern":"1","publisher":"Universität Kassel","_id":"8559","language":[{"iso":"eng"}],"page":"286-293","editor":[{"full_name":"Göller, Robin","last_name":"Göller","first_name":"Robin"},{"last_name":"Biehler","first_name":"Rolf","full_name":"Biehler, Rolf"},{"last_name":"Hochmuth","first_name":"Reinhard","full_name":"Hochmuth, Reinhard"},{"full_name":"Rück, Hans-Georg","first_name":"Hans-Georg","last_name":"Rück"}],"user_id":"30933","author":[{"id":"30933","full_name":"Liebendörfer, Michael","first_name":"Michael","orcid":"0000-0001-9887-2074","last_name":"Liebendörfer"},{"first_name":"Reinhard","last_name":"Hochmuth","full_name":"Hochmuth, Reinhard"}],"title":"Perceived Competence and Incompetence in the First Year of Mathematics Studies: Forms and Situations","year":"2017","status":"public","date_updated":"2022-01-06T07:03:57Z"},{"citation":{"short":"M. Liebendörfer, S. Schukajlow, ZDM 49 (2017) 355–366.","chicago":"Liebendörfer, Michael, and Stanislaw Schukajlow. “Interest Development during the First Year at University: Do Mathematical Beliefs Predict Interest in Mathematics?” <i>ZDM</i> 49, no. 3 (2017): 355–66. <a href=\"https://doi.org/10.1007/s11858-016-0827-3\">https://doi.org/10.1007/s11858-016-0827-3</a>.","apa":"Liebendörfer, M., &#38; Schukajlow, S. (2017). Interest development during the first year at university: do mathematical beliefs predict interest in mathematics? <i>ZDM</i>, <i>49</i>(3), 355–366. <a href=\"https://doi.org/10.1007/s11858-016-0827-3\">https://doi.org/10.1007/s11858-016-0827-3</a>","ieee":"M. Liebendörfer and S. Schukajlow, “Interest development during the first year at university: do mathematical beliefs predict interest in mathematics?,” <i>ZDM</i>, vol. 49, no. 3, pp. 355–366, 2017.","ama":"Liebendörfer M, Schukajlow S. Interest development during the first year at university: do mathematical beliefs predict interest in mathematics? <i>ZDM</i>. 2017;49(3):355-366. doi:<a href=\"https://doi.org/10.1007/s11858-016-0827-3\">10.1007/s11858-016-0827-3</a>","bibtex":"@article{Liebendörfer_Schukajlow_2017, title={Interest development during the first year at university: do mathematical beliefs predict interest in mathematics?}, volume={49}, DOI={<a href=\"https://doi.org/10.1007/s11858-016-0827-3\">10.1007/s11858-016-0827-3</a>}, number={3}, journal={ZDM}, author={Liebendörfer, Michael and Schukajlow, Stanislaw}, year={2017}, pages={355–366} }","mla":"Liebendörfer, Michael, and Stanislaw Schukajlow. “Interest Development during the First Year at University: Do Mathematical Beliefs Predict Interest in Mathematics?” <i>ZDM</i>, vol. 49, no. 3, 2017, pp. 355–66, doi:<a href=\"https://doi.org/10.1007/s11858-016-0827-3\">10.1007/s11858-016-0827-3</a>."},"quality_controlled":"1","status":"public","_id":"8564","page":"355-366","volume":49,"user_id":"30933","publication":"ZDM","issue":"3","extern":"1","date_created":"2019-03-25T15:35:29Z","department":[{"_id":"10"}],"type":"journal_article","author":[{"full_name":"Liebendörfer, Michael","orcid":"0000-0001-9887-2074","first_name":"Michael","last_name":"Liebendörfer","id":"30933"},{"full_name":"Schukajlow, Stanislaw","first_name":"Stanislaw","last_name":"Schukajlow"}],"publication_identifier":{"issn":["1863-9690, 1863-9704"]},"title":"Interest development during the first year at university: do mathematical beliefs predict interest in mathematics?","year":"2017","intvolume":"        49","date_updated":"2022-01-06T07:03:57Z","language":[{"iso":"eng"}],"doi":"10.1007/s11858-016-0827-3"},{"doi":"10.1007/978-3-319-64063-1_7","user_id":"47427","page":"159-182","_id":"8752","language":[{"iso":"eng"}],"date_updated":"2022-01-06T07:04:00Z","publication_status":"published","year":"2017","title":"Gradient-Based Multiobjective Optimization with Uncertainties","status":"public","author":[{"id":"47427","first_name":"Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","full_name":"Peitz, Sebastian"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"}],"publication_identifier":{"isbn":["9783319640624","9783319640631"],"issn":["1860-949X","1860-9503"]},"type":"conference","department":[{"_id":"101"}],"place":"Cham","date_created":"2019-03-29T13:28:56Z","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."}],"project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"publication":"NEO 2016","citation":{"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} }","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>","ieee":"S. Peitz and M. Dellnitz, “Gradient-Based Multiobjective Optimization with Uncertainties,” in <i>NEO 2016</i>, 2017, pp. 159–182.","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>","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>.","short":"S. Peitz, M. Dellnitz, in: NEO 2016, Cham, 2017, pp. 159–182."}},{"date_updated":"2022-01-06T07:03:12Z","author":[{"first_name":"Benjamin","last_name":"Jurgelucks","full_name":"Jurgelucks, Benjamin"},{"full_name":"Feldmann, Nadine","first_name":"Nadine","last_name":"Feldmann","id":"23082"},{"id":"11829","first_name":"Leander","last_name":"Claes","orcid":"0000-0002-4393-268X","full_name":"Claes, Leander"},{"last_name":"Henning","first_name":"Bernd","full_name":"Henning, Bernd","id":"213"},{"first_name":"Andrea","last_name":"Walther","full_name":"Walther, Andrea"}],"title":"Material parameter determination of a piezoelectric disc with triple-ring-electrodes for increased sensitivity","year":"2017","status":"public","user_id":"23082","doi":"10.1121/2.0000707","language":[{"iso":"eng"}],"_id":"6572","page":"030010","project":[{"name":"Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums","_id":"90"}],"citation":{"short":"B. Jurgelucks, N. Feldmann, L. Claes, B. Henning, A. Walther, in: Proceedings of Meetings on Acoustics, Honolulu, 2017, p. 030010.","chicago":"Jurgelucks, Benjamin, Nadine Feldmann, Leander Claes, Bernd Henning, and Andrea Walther. “Material Parameter Determination of a Piezoelectric Disc with Triple-Ring-Electrodes for Increased Sensitivity.” In <i>Proceedings of Meetings on Acoustics</i>, 030010. Honolulu, 2017. <a href=\"https://doi.org/10.1121/2.0000707\">https://doi.org/10.1121/2.0000707</a>.","apa":"Jurgelucks, B., Feldmann, N., Claes, L., Henning, B., &#38; Walther, A. (2017). Material parameter determination of a piezoelectric disc with triple-ring-electrodes for increased sensitivity. In <i>Proceedings of Meetings on Acoustics</i> (p. 030010). Honolulu. <a href=\"https://doi.org/10.1121/2.0000707\">https://doi.org/10.1121/2.0000707</a>","ieee":"B. Jurgelucks, N. Feldmann, L. Claes, B. Henning, and A. Walther, “Material parameter determination of a piezoelectric disc with triple-ring-electrodes for increased sensitivity,” in <i>Proceedings of Meetings on Acoustics</i>, 2017, p. 030010.","ama":"Jurgelucks B, Feldmann N, Claes L, Henning B, Walther A. Material parameter determination of a piezoelectric disc with triple-ring-electrodes for increased sensitivity. In: <i>Proceedings of Meetings on Acoustics</i>. Honolulu; 2017:030010. doi:<a href=\"https://doi.org/10.1121/2.0000707\">10.1121/2.0000707</a>","bibtex":"@inproceedings{Jurgelucks_Feldmann_Claes_Henning_Walther_2017, place={Honolulu}, title={Material parameter determination of a piezoelectric disc with triple-ring-electrodes for increased sensitivity}, DOI={<a href=\"https://doi.org/10.1121/2.0000707\">10.1121/2.0000707</a>}, booktitle={Proceedings of Meetings on Acoustics}, author={Jurgelucks, Benjamin and Feldmann, Nadine and Claes, Leander and Henning, Bernd and Walther, Andrea}, year={2017}, pages={030010} }","mla":"Jurgelucks, Benjamin, et al. “Material Parameter Determination of a Piezoelectric Disc with Triple-Ring-Electrodes for Increased Sensitivity.” <i>Proceedings of Meetings on Acoustics</i>, 2017, p. 030010, doi:<a href=\"https://doi.org/10.1121/2.0000707\">10.1121/2.0000707</a>."},"publication":"Proceedings of Meetings on Acoustics","department":[{"_id":"49"},{"_id":"104"}],"type":"conference","date_created":"2019-01-09T14:37:21Z","place":"Honolulu"},{"date_created":"2020-04-15T08:40:29Z","type":"journal_article","department":[{"_id":"101"}],"publication":"Dynamical Systems","citation":{"bibtex":"@article{Dellnitz_Klus_2017, title={Sensing and control in symmetric networks}, DOI={<a href=\"https://doi.org/10.1080/14689367.2016.1215410\">10.1080/14689367.2016.1215410</a>}, journal={Dynamical Systems}, author={Dellnitz, Michael and Klus, Stefan}, year={2017}, pages={61–79} }","ama":"Dellnitz M, Klus S. Sensing and control in symmetric networks. <i>Dynamical Systems</i>. 2017:61-79. doi:<a href=\"https://doi.org/10.1080/14689367.2016.1215410\">10.1080/14689367.2016.1215410</a>","mla":"Dellnitz, Michael, and Stefan Klus. “Sensing and Control in Symmetric Networks.” <i>Dynamical Systems</i>, 2017, pp. 61–79, doi:<a href=\"https://doi.org/10.1080/14689367.2016.1215410\">10.1080/14689367.2016.1215410</a>.","short":"M. Dellnitz, S. Klus, Dynamical Systems (2017) 61–79.","chicago":"Dellnitz, Michael, and Stefan Klus. “Sensing and Control in Symmetric Networks.” <i>Dynamical Systems</i>, 2017, 61–79. <a href=\"https://doi.org/10.1080/14689367.2016.1215410\">https://doi.org/10.1080/14689367.2016.1215410</a>.","ieee":"M. Dellnitz and S. Klus, “Sensing and control in symmetric networks,” <i>Dynamical Systems</i>, pp. 61–79, 2017.","apa":"Dellnitz, M., &#38; Klus, S. (2017). Sensing and control in symmetric networks. <i>Dynamical Systems</i>, 61–79. <a href=\"https://doi.org/10.1080/14689367.2016.1215410\">https://doi.org/10.1080/14689367.2016.1215410</a>"},"page":"61-79","language":[{"iso":"eng"}],"_id":"16540","user_id":"15701","doi":"10.1080/14689367.2016.1215410","year":"2017","status":"public","title":"Sensing and control in symmetric networks","publication_identifier":{"issn":["1468-9367","1468-9375"]},"author":[{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"},{"full_name":"Klus, Stefan","first_name":"Stefan","last_name":"Klus"}],"publication_status":"published","date_updated":"2022-01-06T06:52:52Z"},{"publication":"SIAM Journal on Applied Dynamical Systems","citation":{"short":"M. Dellnitz, S. Klus, A. Ziessler, SIAM Journal on Applied Dynamical Systems (2017) 120–138.","chicago":"Dellnitz, Michael, Stefan Klus, and Adrian Ziessler. “A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty.” <i>SIAM Journal on Applied Dynamical Systems</i>, 2017, 120–38. <a href=\"https://doi.org/10.1137/16m1072735\">https://doi.org/10.1137/16m1072735</a>.","apa":"Dellnitz, M., Klus, S., &#38; Ziessler, A. (2017). A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty. <i>SIAM Journal on Applied Dynamical Systems</i>, 120–138. <a href=\"https://doi.org/10.1137/16m1072735\">https://doi.org/10.1137/16m1072735</a>","ieee":"M. Dellnitz, S. Klus, and A. Ziessler, “A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty,” <i>SIAM Journal on Applied Dynamical Systems</i>, pp. 120–138, 2017.","ama":"Dellnitz M, Klus S, Ziessler A. A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty. <i>SIAM Journal on Applied Dynamical Systems</i>. 2017:120-138. doi:<a href=\"https://doi.org/10.1137/16m1072735\">10.1137/16m1072735</a>","bibtex":"@article{Dellnitz_Klus_Ziessler_2017, title={A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty}, DOI={<a href=\"https://doi.org/10.1137/16m1072735\">10.1137/16m1072735</a>}, journal={SIAM Journal on Applied Dynamical Systems}, author={Dellnitz, Michael and Klus, Stefan and Ziessler, Adrian}, year={2017}, pages={120–138} }","mla":"Dellnitz, Michael, et al. “A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty.” <i>SIAM Journal on Applied Dynamical Systems</i>, 2017, pp. 120–38, doi:<a href=\"https://doi.org/10.1137/16m1072735\">10.1137/16m1072735</a>."},"date_created":"2020-04-16T05:39:17Z","type":"journal_article","department":[{"_id":"101"}],"year":"2017","status":"public","title":"A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty","author":[{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"},{"full_name":"Klus, Stefan","first_name":"Stefan","last_name":"Klus"},{"first_name":"Adrian","last_name":"Ziessler","full_name":"Ziessler, Adrian"}],"publication_identifier":{"issn":["1536-0040"]},"date_updated":"2022-01-06T06:52:52Z","publication_status":"published","page":"120-138","_id":"16581","language":[{"iso":"eng"}],"doi":"10.1137/16m1072735","user_id":"15701"},{"date_created":"2020-04-16T09:30:56Z","department":[{"_id":"101"}],"type":"journal_article","citation":{"mla":"Peitz, Sebastian, et al. “A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This Research Was Funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (It’s OWL).” <i>IFAC-PapersOnLine</i>, 2017, pp. 8674–79, doi:<a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">10.1016/j.ifacol.2017.08.1526</a>.","ama":"Peitz S, Schäfer K, Ober-Blöbaum S, Eckstein J, Köhler U, Dellnitz M. A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL). <i>IFAC-PapersOnLine</i>. 2017:8674-8679. doi:<a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">10.1016/j.ifacol.2017.08.1526</a>","bibtex":"@article{Peitz_Schäfer_Ober-Blöbaum_Eckstein_Köhler_Dellnitz_2017, title={A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL).}, DOI={<a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">10.1016/j.ifacol.2017.08.1526</a>}, journal={IFAC-PapersOnLine}, author={Peitz, Sebastian and Schäfer, Kai and Ober-Blöbaum, Sina and Eckstein, Julian and Köhler, Ulrich and Dellnitz, Michael}, year={2017}, pages={8674–8679} }","apa":"Peitz, S., Schäfer, K., Ober-Blöbaum, S., Eckstein, J., Köhler, U., &#38; Dellnitz, M. (2017). A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL). <i>IFAC-PapersOnLine</i>, 8674–8679. <a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">https://doi.org/10.1016/j.ifacol.2017.08.1526</a>","ieee":"S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, and M. Dellnitz, “A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL).,” <i>IFAC-PapersOnLine</i>, pp. 8674–8679, 2017.","short":"S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, M. Dellnitz, IFAC-PapersOnLine (2017) 8674–8679.","chicago":"Peitz, Sebastian, Kai Schäfer, Sina Ober-Blöbaum, Julian Eckstein, Ulrich Köhler, and Michael Dellnitz. “A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This Research Was Funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (It’s OWL).” <i>IFAC-PapersOnLine</i>, 2017, 8674–79. <a href=\"https://doi.org/10.1016/j.ifacol.2017.08.1526\">https://doi.org/10.1016/j.ifacol.2017.08.1526</a>."},"publication":"IFAC-PapersOnLine","language":[{"iso":"eng"}],"_id":"16657","page":"8674-8679","doi":"10.1016/j.ifacol.2017.08.1526","user_id":"15701","author":[{"first_name":"Sebastian","last_name":"Peitz","full_name":"Peitz, Sebastian"},{"full_name":"Schäfer, Kai","first_name":"Kai","last_name":"Schäfer"},{"full_name":"Ober-Blöbaum, Sina","first_name":"Sina","last_name":"Ober-Blöbaum"},{"first_name":"Julian","last_name":"Eckstein","full_name":"Eckstein, Julian"},{"full_name":"Köhler, Ulrich","last_name":"Köhler","first_name":"Ulrich"},{"first_name":"Michael","last_name":"Dellnitz","full_name":"Dellnitz, Michael"}],"publication_identifier":{"issn":["2405-8963"]},"status":"public","title":"A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL).","year":"2017","date_updated":"2022-01-06T06:52:53Z","publication_status":"published"},{"file_date_updated":"2020-03-13T12:52:50Z","citation":{"ama":"Peitz S. <i>  Exploiting Structure in Multiobjective Optimization and Optimal Control</i>.; 2017. doi:<a href=\"https://doi.org/10.17619/UNIPB/1-176\">10.17619/UNIPB/1-176</a>","bibtex":"@book{Peitz_2017, title={  Exploiting structure in multiobjective optimization and optimal control}, DOI={<a href=\"https://doi.org/10.17619/UNIPB/1-176\">10.17619/UNIPB/1-176</a>}, author={Peitz, Sebastian}, year={2017} }","mla":"Peitz, Sebastian. <i>  Exploiting Structure in Multiobjective Optimization and Optimal Control</i>. 2017, doi:<a href=\"https://doi.org/10.17619/UNIPB/1-176\">10.17619/UNIPB/1-176</a>.","short":"S. Peitz,   Exploiting Structure in Multiobjective Optimization and Optimal Control, 2017.","chicago":"Peitz, Sebastian. <i>  Exploiting Structure in Multiobjective Optimization and Optimal Control</i>, 2017. <a href=\"https://doi.org/10.17619/UNIPB/1-176\">https://doi.org/10.17619/UNIPB/1-176</a>.","apa":"Peitz, S. (2017). <i>  Exploiting structure in multiobjective optimization and optimal control</i>. <a href=\"https://doi.org/10.17619/UNIPB/1-176\">https://doi.org/10.17619/UNIPB/1-176</a>","ieee":"S. Peitz, <i>  Exploiting structure in multiobjective optimization and optimal control</i>. 2017."},"project":[{"_id":"52","name":"Computing Resources Provided by the Paderborn Center for Parallel Computing"}],"oa":"1","status":"public","has_accepted_license":"1","_id":"10594","user_id":"47427","ddc":["510"],"abstract":[{"text":"Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute\r\nthe set of optimal compromises (the Pareto set) between the conflicting objectives.\r\n\r\nSince – in contrast to the solution of a single objective optimization problem – the\r\nPareto set generally consists of an infinite number of solutions, the computational\r\neffort can quickly become challenging. This is even more the case when many problems have to be solved, when the number of objectives is high, or when the objectives\r\nare costly to evaluate. Consequently, this thesis is devoted to the identification and\r\nexploitation of structure both in the Pareto set and the dynamics of the underlying\r\nmodel as well as to the development of efficient algorithms for solving problems with\r\nadditional parameters, with a high number of objectives or with PDE-constraints.\r\nThese three challenges are addressed in three respective parts.\r\n\r\nIn the first part, predictor-corrector methods are extended to entire Pareto sets.\r\nWhen certain smoothness assumptions are satisfied, then the set of parameter dependent Pareto sets possesses additional structure, i.e. it is a manifold. The tangent\r\nspace can be approximated numerically which yields a direction for the predictor\r\nstep. In the corrector step, the predicted set converges to the Pareto set at a new\r\nparameter value. The resulting algorithm is applied to an example from autonomous\r\ndriving.\r\n\r\nIn the second part, the hierarchical structure of Pareto sets is investigated. When\r\nconsidering a subset of the objectives, the resulting solution is a subset of the Pareto\r\nset of the original problem. Under additional smoothness assumptions, the respective subsets are located on the boundary of the Pareto set of the full problem. This\r\nway, the “skeleton” of a Pareto set can be computed and due to the exponential\r\nincrease in computing time with the number of objectives, the computations of\r\nthese subsets are significantly faster which is demonstrated using an example from\r\nindustrial laundries.\r\n\r\nIn the third part, PDE-constrained multiobjective optimal control problems are\r\naddressed by reduced order modeling methods. Reduced order models exploit the\r\nstructure in the system dynamics, for example by describing the dynamics of only the\r\nmost energetic modes. The model reduction introduces an error in both the function values and their gradients, which has to be taken into account in the development of\r\nalgorithms. Both scalarization and set-oriented approaches are coupled with reduced\r\norder modeling. Convergence results are presented and the numerical benefit is\r\ninvestigated. The algorithms are applied to semi-linear heat flow problems as well\r\nas to the Navier-Stokes equations.\r\n","lang":"eng"}],"file":[{"date_created":"2020-03-13T12:52:50Z","creator":"speitz","file_id":"16298","content_type":"application/pdf","success":1,"relation":"main_file","date_updated":"2020-03-13T12:52:50Z","file_name":"Dissertation_Peitz.pdf","access_level":"closed","file_size":16636801}],"date_created":"2019-07-10T08:12:22Z","type":"dissertation","department":[{"_id":"101"}],"title":" \tExploiting structure in multiobjective optimization and optimal control","year":"2017","author":[{"id":"47427","full_name":"Peitz, Sebastian","orcid":"https://orcid.org/0000-0002-3389-793X","last_name":"Peitz","first_name":"Sebastian"}],"publication_status":"published","date_updated":"2022-01-06T06:50:46Z","main_file_link":[{"open_access":"1","url":"https://d-nb.info/1139356542/34"}],"language":[{"iso":"eng"}],"doi":"10.17619/UNIPB/1-176"},{"publisher":"Springer Spektrum","_id":"31814","edition":"1","page":"17-28","editor":[{"first_name":"J.","last_name":"Leuders","full_name":"Leuders, J."},{"full_name":"Leuders, T.","first_name":"T.","last_name":"Leuders"},{"first_name":"S.","last_name":"Ruwisch","full_name":"Ruwisch, S."},{"full_name":"Prediger, S.","first_name":"S.","last_name":"Prediger"}],"user_id":"85821","status":"public","place":"Wiesbaden","citation":{"ieee":"U. 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