{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T10:51:03Z","timestamp":1775040663408,"version":"3.50.1"},"reference-count":28,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2017,8,18]],"date-time":"2017-08-18T00:00:00Z","timestamp":1503014400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100009160","name":"Universit\u00e9 Toulouse III - Paul Sabatier","doi-asserted-by":"publisher","award":["UID\/MAT\/00324\/2013"],"award-info":[{"award-number":["UID\/MAT\/00324\/2013"]}],"id":[{"id":"10.13039\/501100009160","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009160","name":"Universit\u00e9 Toulouse III - Paul Sabatier","doi-asserted-by":"publisher","award":["SFRH\/BSAB\/114622\/2016"],"award-info":[{"award-number":["SFRH\/BSAB\/114622\/2016"]}],"id":[{"id":"10.13039\/501100009160","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009160","name":"Universit\u00e9 Toulouse III - Paul Sabatier","doi-asserted-by":"publisher","award":["P2020 SAICTPAC\/0011\/2015"],"award-info":[{"award-number":["P2020 SAICTPAC\/0011\/2015"]}],"id":[{"id":"10.13039\/501100009160","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006129","name":"Fuel Cycle Technologies","doi-asserted-by":"publisher","award":["UID\/MAT\/00324\/2013"],"award-info":[{"award-number":["UID\/MAT\/00324\/2013"]}],"id":[{"id":"10.13039\/100006129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006129","name":"Fuel Cycle Technologies","doi-asserted-by":"publisher","award":["SFRH\/BSAB\/114622\/2016"],"award-info":[{"award-number":["SFRH\/BSAB\/114622\/2016"]}],"id":[{"id":"10.13039\/100006129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006129","name":"Fuel Cycle Technologies","doi-asserted-by":"publisher","award":["P2020 SAICTPAC\/0011\/2015"],"award-info":[{"award-number":["P2020 SAICTPAC\/0011\/2015"]}],"id":[{"id":"10.13039\/100006129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004377","name":"Hong Kong Polytechnic University","doi-asserted-by":"publisher","award":["1-ZVHT"],"award-info":[{"award-number":["1-ZVHT"]}],"id":[{"id":"10.13039\/501100004377","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,7,17]]},"DOI":"10.1093\/imanum\/drx043","type":"journal-article","created":{"date-parts":[[2017,7,11]],"date-time":"2017-07-11T15:20:12Z","timestamp":1499786412000},"page":"1579-1597","source":"Crossref","is-referenced-by-count":42,"title":["Complexity and global rates of trust-region methods based on probabilistic models"],"prefix":"10.1093","volume":"38","author":[{"given":"Serge","family":"Gratton","sequence":"first","affiliation":[{"name":"University of Toulouse, IRIT, Rue Charles Camichel, Toulouse Cedex, France"}]},{"given":"Cl\u00e9ment W","family":"Royer","sequence":"additional","affiliation":[{"name":"Wisconsin Institute for Discovery, University of Wisconsin-Madison, USA"}]},{"given":"Lu\u00eds N","family":"Vicente","sequence":"additional","affiliation":[{"name":"CMUC, Department of Mathematics, University of Coimbra, Portugal"}]},{"given":"Zaikun","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China"}]}],"member":"286","published-online":{"date-parts":[[2017,8,18]]},"reference":[{"key":"key\n\t\t\t\t20180717070051_B1","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s10107-012-0578-z","article-title":"Computation of sparse low degree interpolating polynomials and their application to derivative-free optimization.","volume":"134","author":"Bandeira","year":"2012","journal-title":"Math. Program."},{"key":"key\n\t\t\t\t20180717070051_B2","doi-asserted-by":"crossref","first-page":"1238","DOI":"10.1137\/130915984","article-title":"Convergence of trust-region methods based on probabilistic models.","volume":"24","author":"Bandeira","year":"2014","journal-title":"SIAM J. Optim."},{"key":"key\n\t\t\t\t20180717070051_B3","article-title":"Convergence rate analysis of a stochastic trust region method for nonconvex optimization.","author":"Blanchet","year":"2016"},{"key":"key\n\t\t\t\t20180717070051_B4","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.jco.2011.06.001","article-title":"Complexity bounds for second-order optimality in unconstrained optimization.","volume":"28","author":"Cartis","year":"2012","journal-title":"J. Complexity"},{"key":"key\n\t\t\t\t20180717070051_B5","article-title":"Global convergence rate analysis of unconstrained optimization methods based on probabilistic models.","author":"Cartis","year":"2017","journal-title":"Math. Program."},{"key":"key\n\t\t\t\t20180717070051_B6","article-title":"Stochastic optimization using a trust-region method and random models.","author":"Chen","year":"2017","journal-title":"Math. Program."},{"key":"key\n\t\t\t\t20180717070051_B7","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719857","volume-title":"Trust-Region Methods","author":"Conn","year":"2000"},{"key":"key\n\t\t\t\t20180717070051_B8","doi-asserted-by":"crossref","DOI":"10.2514\/6.1998-4718","article-title":"A derivative free optimization algorithm in practice.","volume-title":"Proceedings of the 7th AIAA\/USAF\/NASA\/ISSMO Symposium on Multidisciplinary Analysis and Optimization.","author":"Conn","year":"1998"},{"key":"key\n\t\t\t\t20180717070051_B9","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/s10107-006-0073-5","article-title":"Geometry of interpolation sets in derivative-free optimization.","volume":"111","author":"Conn","year":"2008","journal-title":"Math. Program."},{"key":"key\n\t\t\t\t20180717070051_B10","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1093\/imanum\/drn046","article-title":"Geometry of sample sets in derivative-free optimization: Polynomial regression and underdetermined interpolation.","volume":"28","author":"Conn","year":"2008","journal-title":"IMA J. Numer. Anal."},{"key":"key\n\t\t\t\t20180717070051_B11","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1137\/060673424","article-title":"Global convergence of general derivative-free trust-region algorithms to first and second order critical points.","volume":"20","author":"Conn","year":"2009","journal-title":"SIAM J. Optim."},{"key":"key\n\t\t\t\t20180717070051_B12","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718768","volume-title":"Introduction to Derivative-Free Optimization","author":"Conn","year":"2009"},{"key":"key\n\t\t\t\t20180717070051_B13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10107-016-1026-2","article-title":"A trust region algorithm with a worst-case iteration complexity of ${O}\\left(\\epsilon^{-3\/2}\\right)$ for nonconvex optimization.","volume":"162","author":"Curtis","year":"2017","journal-title":"Math. Program."},{"key":"key\n\t\t\t\t20180717070051_B14","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611974683.ch37","article-title":"Methodologies and software for derivative-free optimization.","volume-title":"Advances and Trends in Optimization with Engineering Applications","author":"Cust\u00f3dio","year":"2017"},{"key":"key\n\t\t\t\t20180717070051_B15","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1080\/10556780802409296","article-title":"On the geometry phase in model-based algorithms for derivative-free optimization.","volume":"24","author":"Fasano","year":"2009","journal-title":"Optim. Methods Softw."},{"key":"key\n\t\t\t\t20180717070051_B16","doi-asserted-by":"crossref","first-page":"1987","DOI":"10.1137\/151005683","article-title":"Trust-region methods without using derivatives: worst case complexity and the non-smooth case.","volume":"26","author":"Garmanjani","year":"2016","journal-title":"SIAM J. Optim."},{"key":"key\n\t\t\t\t20180717070051_B17","doi-asserted-by":"crossref","first-page":"980","DOI":"10.1007\/s10957-016-1007-x","article-title":"Nonlinear stepsize control algorithms: complexity bounds for first- and second-order optimality.","volume":"171","author":"Grapiglia","year":"2016","journal-title":"J. Optim. Theory Appl."},{"key":"key\n\t\t\t\t20180717070051_B18","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1080\/10556788.2015.1130129","article-title":"On the worst-case complexity of nonlinear stepsize control algorithms for convex unconstrained optimization.","volume":"31","author":"Grapiglia","year":"2016","journal-title":"Optim. Methods Softw."},{"key":"key\n\t\t\t\t20180717070051_B19","doi-asserted-by":"crossref","first-page":"1515","DOI":"10.1137\/140961602","article-title":"Direct search based on probabilistic descent.","volume":"25","author":"Gratton","year":"2015","journal-title":"SIAM J. Optim."},{"key":"key\n\t\t\t\t20180717070051_B20","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1137\/050623012","article-title":"Recursive trust-region methods for multiscale nonlinear optimization.","volume":"19","author":"Gratton","year":"2008","journal-title":"SIAM J. Optim."},{"key":"key\n\t\t\t\t20180717070051_B21","article-title":"Trust-region methods without using derivatives: worst case complexity and the non-smooth case.","volume-title":"Ph.D. Thesis","author":"J\u00fadice","year":"2015"},{"key":"key\n\t\t\t\t20180717070051_B22","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1007\/s10589-016-9827-z","article-title":"Stochastic derivative-free optimization using a trust region framework.","volume":"64","author":"Larson","year":"2016","journal-title":"Comput. Optim. Appl."},{"key":"key\n\t\t\t\t20180717070051_B23","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s10107-003-0490-7","article-title":"Least Frobenius norm updating of quadratic models that satisfy interpolation conditions.","volume":"100","author":"Powell","year":"2004","journal-title":"Math. Program."},{"key":"key\n\t\t\t\t20180717070051_B24","article-title":"Derivative-free optimization methods based on probabilistic and deterministic properties: complexity analysis and numerical relevance.","volume-title":"Ph.D. Thesis","author":"Royer","year":"2016"},{"key":"key\n\t\t\t\t20180717070051_B25","doi-asserted-by":"crossref","first-page":"3512","DOI":"10.1137\/090748536","article-title":"Self-correcting geometry in model-based algorithms for derivative-free unconstrained optimization.","volume":"20","author":"Scheinberg","year":"2010","journal-title":"SIAM J. Optim."},{"key":"key\n\t\t\t\t20180717070051_B26","article-title":"ASTRO-DF: a class of adaptive sampling trust-region algorithms for derivative-free stochastic optimization.","author":"Shashaani","year":"2016"},{"key":"key\n\t\t\t\t20180717070051_B27","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s13675-012-0003-7","article-title":"Worst case complexity of direct search.","volume":"1","author":"Vicente","year":"2013","journal-title":"EURO J. Comput. Optim."},{"key":"key\n\t\t\t\t20180717070051_B28","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s10107-015-0893-2","article-title":"Recent advances in trust region algorithms.","volume":"151","author":"Yuan","year":"2015","journal-title":"Math. Program."}],"container-title":["IMA Journal of Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/imajna\/article-pdf\/38\/3\/1579\/25170882\/drx043.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,29]],"date-time":"2019-09-29T11:12:01Z","timestamp":1569755521000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/imajna\/article\/38\/3\/1579\/4084726"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,18]]},"references-count":28,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,8,18]]},"published-print":{"date-parts":[[2018,7,17]]}},"URL":"https:\/\/doi.org\/10.1093\/imanum\/drx043","relation":{},"ISSN":["0272-4979","1464-3642"],"issn-type":[{"value":"0272-4979","type":"print"},{"value":"1464-3642","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2018,7]]},"published":{"date-parts":[[2017,8,18]]}}}