{"citation":{"short":"M.B. Berkemeier, S. Peitz, Mathematical and Computational Applications 26 (2021).","chicago":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models.” <i>Mathematical and Computational Applications</i> 26, no. 2 (2021). <a href=\"https://doi.org/10.3390/mca26020031\">https://doi.org/10.3390/mca26020031</a>.","apa":"Berkemeier, M. B., &#38; Peitz, S. (2021). Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models. <i>Mathematical and Computational Applications</i>, <i>26</i>(2). <a href=\"https://doi.org/10.3390/mca26020031\">https://doi.org/10.3390/mca26020031</a>","ieee":"M. B. Berkemeier and S. Peitz, “Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models,” <i>Mathematical and Computational Applications</i>, vol. 26, no. 2, 2021.","bibtex":"@article{Berkemeier_Peitz_2021, title={Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models}, volume={26}, DOI={<a href=\"https://doi.org/10.3390/mca26020031\">10.3390/mca26020031</a>}, number={231}, journal={Mathematical and Computational Applications}, author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2021} }","mla":"Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models.” <i>Mathematical and Computational Applications</i>, vol. 26, no. 2, 31, 2021, doi:<a href=\"https://doi.org/10.3390/mca26020031\">10.3390/mca26020031</a>.","ama":"Berkemeier MB, Peitz S. Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models. <i>Mathematical and Computational Applications</i>. 2021;26(2). doi:<a href=\"https://doi.org/10.3390/mca26020031\">10.3390/mca26020031</a>"},"publication":"Mathematical and Computational Applications","issue":"2","publication_status":"published","department":[{"_id":"101"},{"_id":"655"}],"publication_identifier":{"eissn":["2297-8747"]},"intvolume":"        26","oa":"1","type":"journal_article","volume":26,"date_updated":"2022-01-06T06:54:55Z","_id":"21337","language":[{"iso":"eng"}],"title":"Derivative-Free Multiobjective Trust Region Descent Method Using Radial  Basis Function Surrogate Models","author":[{"full_name":"Berkemeier, Manuel Bastian","last_name":"Berkemeier","first_name":"Manuel Bastian","id":"51701"},{"id":"47427","first_name":"Sebastian","last_name":"Peitz","full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X"}],"year":"2021","main_file_link":[{"open_access":"1","url":"https://www.mdpi.com/2297-8747/26/2/31/pdf"}],"user_id":"47427","article_number":"31","date_created":"2021-03-01T10:46:48Z","status":"public","abstract":[{"lang":"eng","text":"We present a flexible trust region descend algorithm for unconstrained and\r\nconvexly constrained multiobjective optimization problems. It is targeted at\r\nheterogeneous and expensive problems, i.e., problems that have at least one\r\nobjective function that is computationally expensive. The method is\r\nderivative-free in the sense that neither need derivative information be\r\navailable for the expensive objectives nor are gradients approximated using\r\nrepeated function evaluations as is the case in finite-difference methods.\r\nInstead, a multiobjective trust region approach is used that works similarly to\r\nits well-known scalar pendants. Local surrogate models constructed from\r\nevaluation data of the true objective functions are employed to compute\r\npossible descent directions. In contrast to existing multiobjective trust\r\nregion algorithms, these surrogates are not polynomial but carefully\r\nconstructed radial basis function networks. This has the important advantage\r\nthat the number of data points scales linearly with the parameter space\r\ndimension. The local models qualify as fully linear and the corresponding\r\ngeneral scalar framework is adapted for problems with multiple objectives.\r\nConvergence to Pareto critical points is proven and numerical examples\r\nillustrate our findings."}],"doi":"10.3390/mca26020031"}