{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/pdf/2210.04579"}],"language":[{"iso":"eng"}],"publication":"arXiv:2210.04579","type":"preprint","date_updated":"2022-12-20T15:28:54Z","oa":"1","abstract":[{"lang":"eng","text":"In this article, we show how second-order derivative information can be\r\nincorporated into gradient sampling methods for nonsmooth optimization. The\r\nsecond-order information we consider is essentially the set of coefficients of\r\nall second-order Taylor expansions of the objective in a closed ball around a\r\ngiven point. Based on this concept, we define a model of the objective as the\r\nmaximum of these Taylor expansions. Iteratively minimizing this model\r\n(constrained to the closed ball) results in a simple descent method, for which\r\nwe prove convergence to minimal points in case the objective is convex. To\r\nobtain an implementable method, we construct an approximation scheme for the\r\nsecond-order information based on sampling objective values, gradients and\r\nHessian matrices at finitely many points. Using a set of test problems, we\r\ncompare the resulting method to five other available solvers. Considering the\r\nnumber of function evaluations, the results suggest that the method we propose\r\nis superior to the standard gradient sampling method, and competitive compared\r\nto other methods."}],"author":[{"first_name":"Bennet","last_name":"Gebken","id":"32643","full_name":"Gebken, Bennet"}],"year":"2022","status":"public","date_created":"2022-12-20T15:25:17Z","citation":{"bibtex":"@article{Gebken_2022, title={Using second-order information in gradient sampling methods for  nonsmooth optimization}, journal={arXiv:2210.04579}, author={Gebken, Bennet}, year={2022} }","chicago":"Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods for  Nonsmooth Optimization.” <i>ArXiv:2210.04579</i>, 2022.","short":"B. Gebken, ArXiv:2210.04579 (2022).","mla":"Gebken, Bennet. “Using Second-Order Information in Gradient Sampling Methods for  Nonsmooth Optimization.” <i>ArXiv:2210.04579</i>, 2022.","ama":"Gebken B. Using second-order information in gradient sampling methods for  nonsmooth optimization. <i>arXiv:221004579</i>. Published online 2022.","ieee":"B. Gebken, “Using second-order information in gradient sampling methods for  nonsmooth optimization,” <i>arXiv:2210.04579</i>. 2022.","apa":"Gebken, B. (2022). Using second-order information in gradient sampling methods for  nonsmooth optimization. In <i>arXiv:2210.04579</i>."},"external_id":{"arxiv":["2210.04579"]},"user_id":"32643","department":[{"_id":"101"}],"_id":"34618","title":"Using second-order information in gradient sampling methods for  nonsmooth optimization"}