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A further improvement in terms of efficiency is achieved by avoiding the solution of a quadratic subproblem to compute a common step direction for all objective functions, which is usually required in first-order methods. Using a different discretization of our inertial gradient-like dynamical system, we obtain an accelerated multiobjective gradient method that does not require the solution of a subproblem in each step (Algorithm 2). While this algorithm does not converge in general, it yields good results on test problems while being faster than standard steepest descent."}],"title":"Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems","user_id":"56399","author":[{"orcid":"https://orcid.org/0000-0003-3384-3496","full_name":"Sonntag, Konstantin","first_name":"Konstantin","id":"56399","last_name":"Sonntag"},{"id":"47427","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","first_name":"Sebastian"}],"publisher":"Springer","department":[{"_id":"101"},{"_id":"655"}],"publication":"Journal of Optimization Theory and Applications","publication_status":"published","status":"public","date_created":"2023-07-12T06:35:58Z","date_updated":"2024-02-21T10:13:33Z","_id":"46019","doi":"10.1007/s10957-024-02389-3","oa":"1","main_file_link":[{"url":"https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf","open_access":"1"}],"year":"2024","citation":{"ieee":"K. Sonntag and S. Peitz, “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems,” Journal of Optimization Theory and Applications, 2024, doi: 10.1007/s10957-024-02389-3.","short":"K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024).","bibtex":"@article{Sonntag_Peitz_2024, title={Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems}, DOI={10.1007/s10957-024-02389-3}, journal={Journal of Optimization Theory and Applications}, publisher={Springer}, author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024} }","mla":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal of Optimization Theory and Applications, Springer, 2024, doi:10.1007/s10957-024-02389-3.","ama":"Sonntag K, Peitz S. Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications. Published online 2024. doi:10.1007/s10957-024-02389-3","apa":"Sonntag, K., & Peitz, S. (2024). Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications. https://doi.org/10.1007/s10957-024-02389-3","chicago":"Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal of Optimization Theory and Applications, 2024. https://doi.org/10.1007/s10957-024-02389-3."},"type":"journal_article","language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"citation":{"ama":"Sonntag K, Gebken B, Müller G, Peitz S, Volkwein S. A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces. arXiv:240206376. Published online 2024.","apa":"Sonntag, K., Gebken, B., Müller, G., Peitz, S., & Volkwein, S. (2024). A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces. In arXiv:2402.06376.","chicago":"Sonntag, Konstantin, Bennet Gebken, Georg Müller, Sebastian Peitz, and Stefan Volkwein. “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024.","bibtex":"@article{Sonntag_Gebken_Müller_Peitz_Volkwein_2024, title={A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces}, journal={arXiv:2402.06376}, author={Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian and Volkwein, Stefan}, year={2024} }","mla":"Sonntag, Konstantin, et al. “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024.","short":"K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376 (2024).","ieee":"K. Sonntag, B. Gebken, G. Müller, S. Peitz, and S. Volkwein, “A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces,” arXiv:2402.06376. 2024."},"type":"preprint","year":"2024","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2402.06376"}],"oa":"1","date_updated":"2024-02-21T10:21:03Z","_id":"51334","status":"public","has_accepted_license":"1","date_created":"2024-02-13T09:35:26Z","author":[{"id":"56399","last_name":"Sonntag","full_name":"Sonntag, Konstantin","orcid":"https://orcid.org/0000-0003-3384-3496","first_name":"Konstantin"},{"full_name":"Gebken, Bennet","first_name":"Bennet","id":"32643","last_name":"Gebken"},{"last_name":"Müller","first_name":"Georg","full_name":"Müller, Georg"},{"id":"47427","last_name":"Peitz","orcid":"0000-0002-3389-793X","full_name":"Peitz, Sebastian","first_name":"Sebastian"},{"last_name":"Volkwein","first_name":"Stefan","full_name":"Volkwein, Stefan"}],"department":[{"_id":"101"},{"_id":"655"}],"publication":"arXiv:2402.06376","user_id":"56399","title":"A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces","abstract":[{"lang":"eng","text":"The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points, where in each iteration, an approximation of the subdifferential is computed in an efficient manner and then used to compute a common descent direction for all objective functions. To prove convergence, we present some new optimality results for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these, we can show that every accumulation point of the sequence generated by our algorithm is Pareto critical under common assumptions. Computational efficiency for finding Pareto critical points is numerically demonstrated for multiobjective optimal control of an obstacle problem."}],"external_id":{"arxiv":["\t2402.06376"]}},{"date_created":"2024-02-21T16:12:42Z","status":"public","department":[{"_id":"9"},{"_id":"150"}],"author":[{"full_name":"Bablitzka, Nico Janosch","first_name":"Nico Janosch","last_name":"Bablitzka"},{"id":"45788","last_name":"Beimdiek","full_name":"Beimdiek, Janis","first_name":"Janis"}],"user_id":"45788","title":"Einfluss von Temperatur und Strömungsführung auf die NH3-SCO sowie die NH3-SCR mit Partikeln aus einer Sprayflammensynthese","place":"Paderborn","language":[{"iso":"ger"}],"supervisor":[{"first_name":"Janis","full_name":"Beimdiek, Janis","last_name":"Beimdiek","id":"45788"},{"last_name":"Schmid","id":"464","first_name":"Hans-Joachim","orcid":"000-0001-8590-1921","full_name":"Schmid, Hans-Joachim"},{"last_name":"Schiller","first_name":"Sascha","full_name":"Schiller, Sascha"}],"citation":{"mla":"Bablitzka, Nico Janosch, and Janis Beimdiek. Einfluss von Temperatur und Strömungsführung auf die NH3-SCO sowie die NH3-SCR mit Partikeln aus einer Sprayflammensynthese. 2024.","bibtex":"@book{Bablitzka_Beimdiek_2024, place={Paderborn}, title={Einfluss von Temperatur und Strömungsführung auf die NH3-SCO sowie die NH3-SCR mit Partikeln aus einer Sprayflammensynthese}, author={Bablitzka, Nico Janosch and Beimdiek, Janis}, year={2024} }","chicago":"Bablitzka, Nico Janosch, and Janis Beimdiek. Einfluss von Temperatur und Strömungsführung auf die NH3-SCO sowie die NH3-SCR mit Partikeln aus einer Sprayflammensynthese. Paderborn, 2024.","ama":"Bablitzka NJ, Beimdiek J. Einfluss von Temperatur und Strömungsführung auf die NH3-SCO sowie die NH3-SCR mit Partikeln aus einer Sprayflammensynthese.; 2024.","apa":"Bablitzka, N. J., & Beimdiek, J. (2024). Einfluss von Temperatur und Strömungsführung auf die NH3-SCO sowie die NH3-SCR mit Partikeln aus einer Sprayflammensynthese.","ieee":"N. J. Bablitzka and J. Beimdiek, Einfluss von Temperatur und Strömungsführung auf die NH3-SCO sowie die NH3-SCR mit Partikeln aus einer Sprayflammensynthese. Paderborn, 2024.","short":"N.J. Bablitzka, J. Beimdiek, Einfluss von Temperatur und Strömungsführung auf die NH3-SCO sowie die NH3-SCR mit Partikeln aus einer Sprayflammensynthese, Paderborn, 2024."},"type":"bachelorsthesis","year":"2024","_id":"51724","date_updated":"2024-02-21T16:13:00Z"},{"abstract":[{"lang":"eng","text":"Estimating the infection risks in indoor environments comprises the assessment of the behavior of virus-laden aerosols, i.e. spreading, mixing, removal by air purifiers etc. A promising experimental approach is based on using non-hazardous surrogate aerosols of similar size, e.g. salt particles, to mimic the virus aerosol behavior. This manuscript addresses the issue how a successful transfer of such experiments can be accomplished. Corresponding experiments in two very different environments, a large community hall and a seminar room, with optional use of air purifiers in various constellations were conducted. While high particle concentrations are advantageous in terms of avoiding influence of background aerosol concentrations, it is shown that appropriate consideration of aggregation and settling are vital to theoretically describe the experimentally determined course of particle concentrations. A corresponding model equation for a well-mixed situation is derived and the required parameters are thoroughly determined in separate experiments independently. It is demonstrated that clean air delivery rates (CADR) of air purifiers determined with this approach may differ substantially from common approaches not explicitly taking into account aggregation. "}],"user_id":"45788","title":"Evaluation of Surrogate Aerosol Experiments to Predict Spreading and Removal of Virus-Laden Aerosols","department":[{"_id":"150"},{"_id":"9"}],"publication":"Atmosphere","keyword":["surrogate aerosols","indoor air cleaners","ultra-fine particles","COVID-19","test method","field experiments: clean air delivery rate"],"author":[{"last_name":"Beimdiek","id":"45788","first_name":"Janis","full_name":"Beimdiek, Janis"},{"last_name":"Schmid","id":"464","first_name":"Hans-Joachim","full_name":"Schmid, Hans-Joachim","orcid":"000-0001-8590-1921"}],"publisher":"MDPI","date_created":"2024-02-21T16:38:06Z","status":"public","date_updated":"2024-02-21T16:38:20Z","_id":"51731","oa":"1","main_file_link":[{"url":"https://doi.org/10.20944/preprints202401.1858.v1","open_access":"1"}],"language":[{"iso":"eng"}],"citation":{"chicago":"Beimdiek, Janis, and Hans-Joachim Schmid. “Evaluation of Surrogate Aerosol Experiments to Predict Spreading and Removal of Virus-Laden Aerosols.” Atmosphere. MDPI, 2024.","ama":"Beimdiek J, Schmid H-J. Evaluation of Surrogate Aerosol Experiments to Predict Spreading and Removal of Virus-Laden Aerosols. Atmosphere. Published online 2024.","apa":"Beimdiek, J., & Schmid, H.-J. (2024). Evaluation of Surrogate Aerosol Experiments to Predict Spreading and Removal of Virus-Laden Aerosols. In Atmosphere. MDPI.","bibtex":"@article{Beimdiek_Schmid_2024, title={Evaluation of Surrogate Aerosol Experiments to Predict Spreading and Removal of Virus-Laden Aerosols}, journal={Atmosphere}, publisher={MDPI}, author={Beimdiek, Janis and Schmid, Hans-Joachim}, year={2024} }","mla":"Beimdiek, Janis, and Hans-Joachim Schmid. “Evaluation of Surrogate Aerosol Experiments to Predict Spreading and Removal of Virus-Laden Aerosols.” Atmosphere, MDPI, 2024.","short":"J. Beimdiek, H.-J. Schmid, Atmosphere (2024).","ieee":"J. Beimdiek and H.-J. Schmid, “Evaluation of Surrogate Aerosol Experiments to Predict Spreading and Removal of Virus-Laden Aerosols,” Atmosphere. MDPI, 2024."},"type":"preprint","year":"2024"},{"year":"2024","citation":{"apa":"Richters, M. (2024). Herstellung und Charakterisierung von Wood-Plastic-Composites (WPC) mit einer Matrix aus thermoplastischen Polyurethanen zur Erzeugung einer Holz-WPC-Verbundstruktur .","ama":"Richters M. Herstellung und Charakterisierung von Wood-Plastic-Composites (WPC) mit einer Matrix aus thermoplastischen Polyurethanen zur Erzeugung einer Holz-WPC-Verbundstruktur .; 2024.","chicago":"Richters, Maximilian. Herstellung und Charakterisierung von Wood-Plastic-Composites (WPC) mit einer Matrix aus thermoplastischen Polyurethanen zur Erzeugung einer Holz-WPC-Verbundstruktur , 2024.","bibtex":"@book{Richters_2024, title={Herstellung und Charakterisierung von Wood-Plastic-Composites (WPC) mit einer Matrix aus thermoplastischen Polyurethanen zur Erzeugung einer Holz-WPC-Verbundstruktur }, author={Richters, Maximilian}, year={2024} }","mla":"Richters, Maximilian. Herstellung und Charakterisierung von Wood-Plastic-Composites (WPC) mit einer Matrix aus thermoplastischen Polyurethanen zur Erzeugung einer Holz-WPC-Verbundstruktur . 2024.","short":"M. Richters, Herstellung und Charakterisierung von Wood-Plastic-Composites (WPC) mit einer Matrix aus thermoplastischen Polyurethanen zur Erzeugung einer Holz-WPC-Verbundstruktur , 2024.","ieee":"M. Richters, Herstellung und Charakterisierung von Wood-Plastic-Composites (WPC) mit einer Matrix aus thermoplastischen Polyurethanen zur Erzeugung einer Holz-WPC-Verbundstruktur . 2024."},"type":"dissertation","language":[{"iso":"ger"}],"_id":"51732","date_updated":"2024-02-21T18:09:39Z","department":[{"_id":"147"},{"_id":"9"},{"_id":"321"}],"author":[{"first_name":"Maximilian","full_name":"Richters, Maximilian","last_name":"Richters"}],"publication_identifier":{"unknown":["978-3-8440-9390-2"]},"publication_status":"published","date_created":"2024-02-21T18:03:11Z","status":"public","extern":"1","title":"Herstellung und Charakterisierung von Wood-Plastic-Composites (WPC) mit einer Matrix aus thermoplastischen Polyurethanen zur Erzeugung einer Holz-WPC-Verbundstruktur ","user_id":"38221"},{"page":"70-72","citation":{"apa":"Schroeter-Wittke, H. (2024). Seven Psalms. Paul Simons theologische Kammermusik. Praktische Theologie, 59(1), 70–72.","ama":"Schroeter-Wittke H. Seven Psalms. Paul Simons theologische Kammermusik. Praktische Theologie. 2024;59(1):70-72.","chicago":"Schroeter-Wittke, Harald. “Seven Psalms. Paul Simons Theologische Kammermusik.” Praktische Theologie 59, no. 1 (2024): 70–72.","bibtex":"@article{Schroeter-Wittke_2024, title={Seven Psalms. Paul Simons theologische Kammermusik}, volume={59}, number={1}, journal={Praktische Theologie}, author={Schroeter-Wittke, Harald}, year={2024}, pages={70–72} }","mla":"Schroeter-Wittke, Harald. “Seven Psalms. Paul Simons Theologische Kammermusik.” Praktische Theologie, vol. 59, no. 1, 2024, pp. 70–72.","short":"H. Schroeter-Wittke, Praktische Theologie 59 (2024) 70–72.","ieee":"H. Schroeter-Wittke, “Seven Psalms. Paul Simons theologische Kammermusik,” Praktische Theologie, vol. 59, no. 1, pp. 70–72, 2024."},"type":"journal_article","year":"2024","language":[{"iso":"eng"}],"_id":"51733","date_updated":"2024-02-22T00:18:34Z","intvolume":" 59","issue":"1","publication":"Praktische Theologie","author":[{"full_name":"Schroeter-Wittke, Harald","first_name":"Harald","id":"480","last_name":"Schroeter-Wittke"}],"volume":59,"date_created":"2024-02-22T00:18:25Z","status":"public","title":"Seven Psalms. Paul Simons theologische Kammermusik","user_id":"480"}]