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Softw."],"published-print":{"date-parts":[[2023,12,31]]},"abstract":"<jats:p>\n            This article defines an efficient subspace method, called\n            <jats:monospace>SSDFO<\/jats:monospace>\n            , for unconstrained derivative-free optimization problems where the gradients of the objective function are Lipschitz continuous but only exact function values are available.\n            <jats:monospace>SSDFO<\/jats:monospace>\n            employs line searches along directions constructed on the basis of quadratic models. These approximate the objective function in a subspace spanned by some previous search directions. A worst-case complexity bound on the number of iterations and function evaluations is derived for a basic algorithm using this technique. Numerical results for a practical variant with additional heuristic features show that, on the unconstrained\n            <jats:monospace>CUTEst<\/jats:monospace>\n            test problems,\n            <jats:monospace>SSDFO<\/jats:monospace>\n            has superior performance compared to the best solvers from the literature.\n          <\/jats:p>","DOI":"10.1145\/3618297","type":"journal-article","created":{"date-parts":[[2023,9,2]],"date-time":"2023-09-02T11:57:07Z","timestamp":1693655827000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["New Subspace Method for Unconstrained Derivative-Free Optimization"],"prefix":"10.1145","volume":"49","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7973-3770","authenticated-orcid":false,"given":"Morteza","family":"Kimiaei","sequence":"first","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Wien, Austria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8328-9641","authenticated-orcid":false,"given":"Arnold","family":"Neumaier","sequence":"additional","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Wien, Austria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0091-8172","authenticated-orcid":false,"given":"Parvaneh","family":"Faramarzi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Razi University, Iran"}]}],"member":"320","published-online":{"date-parts":[[2023,12,15]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/bf00940566"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-68913-5"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1145\/3544489"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-012-0578-z"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/18m1177718"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-021-09513-z"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1145\/3377929.3389870"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719857"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718768"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s101070100263"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-014-9687-3"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1137\/140961602"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2010.549231"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.5555\/61743"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1137\/0614023"},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970920"},{"key":"e_1_3_1_18_2","unstructured":"M. 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