{"language":[{"iso":"eng"}],"date_updated":"2022-08-26T06:12:10Z","title":"Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients","abstract":[{"lang":"eng","text":"In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the filter method known from single-objective optimization. Instead of the true objective and constraint functions, so-called fully linear models are employed and we show how to deal with the gradient inexactness in the composite step setting, adapted from single-objective optimization as well. Under standard assumptions, we prove convergence of a subset of iterates to a quasi-stationary point and if constraint qualifications hold, then the limit point is also a KKT-point of the multi-objective problem."}],"publication":"arXiv:2208.12094","external_id":{"arxiv":["2208.12094"]},"date_created":"2022-08-26T06:08:06Z","status":"public","_id":"33150","user_id":"47427","main_file_link":[{"url":"https://arxiv.org/pdf/2208.12094","open_access":"1"}],"author":[{"first_name":"Manuel Bastian","id":"51701","full_name":"Berkemeier, Manuel Bastian","last_name":"Berkemeier"},{"first_name":"Sebastian","id":"47427","full_name":"Peitz, Sebastian","last_name":"Peitz","orcid":"0000-0002-3389-793X"}],"year":"2022","oa":"1","type":"preprint","citation":{"mla":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints Using Inexact Gradients.” <i>ArXiv:2208.12094</i>, 2022.","chicago":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints Using Inexact Gradients.” <i>ArXiv:2208.12094</i>, 2022.","apa":"Berkemeier, M. B., &#38; Peitz, S. (2022). Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients. In <i>arXiv:2208.12094</i>.","short":"M.B. Berkemeier, S. Peitz, ArXiv:2208.12094 (2022).","bibtex":"@article{Berkemeier_Peitz_2022, title={Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients}, journal={arXiv:2208.12094}, author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2022} }","ieee":"M. B. Berkemeier and S. Peitz, “Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients,” <i>arXiv:2208.12094</i>. 2022.","ama":"Berkemeier MB, Peitz S. Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using Inexact Gradients. <i>arXiv:220812094</i>. Published online 2022."},"department":[{"_id":"101"},{"_id":"655"}]}