{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T12:47:36Z","timestamp":1771505256598,"version":"3.50.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T00:00:00Z","timestamp":1673222400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T00:00:00Z","timestamp":1673222400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2023,2]]},"DOI":"10.1007\/s10957-022-02153-5","type":"journal-article","created":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T13:11:05Z","timestamp":1673269865000},"page":"700-729","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["The Impact of Noise on Evaluation Complexity: The Deterministic Trust-Region Case"],"prefix":"10.1007","volume":"196","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3691-7836","authenticated-orcid":false,"given":"Stefania","family":"Bellavia","sequence":"first","affiliation":[]},{"given":"Gianmarco","family":"Gurioli","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9213-3622","authenticated-orcid":false,"given":"Benedetta","family":"Morini","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6166-1860","authenticated-orcid":false,"given":"Philippe Louis","family":"Toint","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,1,9]]},"reference":[{"issue":"3","key":"2153_CR1","doi-asserted-by":"crossref","first-page":"1238","DOI":"10.1137\/130915984","volume":"24","author":"AS Bandeira","year":"2014","unstructured":"Bandeira, A.S., Scheinberg, K., Vicente, L.N.: Convergence of trust-region methods based on probabilistic models. SIAM J. Optim. 24(3), 1238\u20131264 (2014)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"2153_CR2","first-page":"227","volume":"71","author":"S Bellavia","year":"2022","unstructured":"Bellavia, S., Gurioli, G.: Complexity analysis of a stochastic cubic regularisation method under inexact gradient evaluations and dynamic Hessian accuracy. Optimization A Journal of Mathematical Programming and Operations Research 71(1), 227\u2013261 (2022)","journal-title":"Optimization A Journal of Mathematical Programming and Operations Research"},{"issue":"1","key":"2153_CR3","doi-asserted-by":"crossref","first-page":"764","DOI":"10.1093\/imanum\/drz076","volume":"41","author":"S Bellavia","year":"2021","unstructured":"Bellavia, S., Gurioli, G., Morini, B.: Adaptive cubic regularization methods with dynamic inexact Hessian information and applications to finite-sum minimization. IMA J. Numer. Anal. 41(1), 764\u2013799 (2021)","journal-title":"IMA J. Numer. Anal."},{"issue":"4","key":"2153_CR4","doi-asserted-by":"crossref","first-page":"2881","DOI":"10.1137\/18M1226282","volume":"29","author":"S Bellavia","year":"2019","unstructured":"Bellavia, S., Gurioli, G., Morini, B., Toint, P.L.: Adaptive regularization algorithms with inexact evaluations for nonconvex optimization. SIAM J. Optim. 29(4), 2881\u20132915 (2019)","journal-title":"SIAM J. Optim."},{"key":"2153_CR5","doi-asserted-by":"crossref","DOI":"10.1016\/j.jco.2021.101591","volume":"68","author":"S Bellavia","year":"2022","unstructured":"Bellavia, S., Gurioli, G., Morini, B., Toint, P.L.: Adaptive regularization for nonconvex optimization using inexact function values and randomly perturbed derivatives. J. Complex. 68, 101591 (2022)","journal-title":"J. Complex."},{"issue":"2","key":"2153_CR6","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.1137\/19M1291832","volume":"31","author":"A Berahas","year":"2021","unstructured":"Berahas, A., Cao, L., Scheinberg, K.: Global convergence rate analysis of a generic line search algorithm with noise. SIAM J. Optim. 31(2), 1489\u20131518 (2021)","journal-title":"SIAM J. Optim."},{"key":"2153_CR7","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1090\/mcom\/3246","volume":"87","author":"EG Birgin","year":"2018","unstructured":"Birgin, E.G., Kreji\u0107, N., Mart\u00ednez, J.M.: On the employment of inexact restoration for the minimization of functions whose evaluation is subject to errors. Math. Comput. 87, 1307\u20131326 (2018)","journal-title":"Math. Comput."},{"key":"2153_CR8","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1090\/mcom\/3445","volume":"89","author":"EG Birgin","year":"2020","unstructured":"Birgin, E.G., Kreji\u0107, N., Mart\u00ednez, J.M.: Iteration and evaluation complexity on the minimization of functions whose computation is intrinsically inexact. Math. Comput. 89, 253\u2013278 (2020)","journal-title":"Math. Comput."},{"issue":"2","key":"2153_CR9","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1287\/ijoo.2019.0016","volume":"1","author":"J Blanchet","year":"2019","unstructured":"Blanchet, J., Cartis, C., Menickelly, M., Scheinberg, K.: Convergence rate analysis of a stochastic trust region method via supermartingales. INFORMS J. Optim. 1(2), 92\u2013119 (2019)","journal-title":"INFORMS J. Optim."},{"key":"2153_CR10","unstructured":"Buckley, AG.: Test functions for unconstrained minimization. Technical Report CS-3. Computing Science Division, Dalhousie University, Dalhousie, Canada (1989)"},{"issue":"1","key":"2153_CR11","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1137\/0728014","volume":"28","author":"RG Carter","year":"1991","unstructured":"Carter, R.G.: On the global convergence of trust region methods using inexact gradient information. SIAM J. Numer. Anal. 28(1), 251\u2013265 (1991)","journal-title":"SIAM J. Numer. Anal."},{"issue":"6","key":"2153_CR12","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1080\/10556788.2016.1268136","volume":"6","author":"C Cartis","year":"2017","unstructured":"Cartis, C., Gould, N.I.M., Toint, P.L.: Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using H\u00f6lder continuous gradients. Optim. Methods Softw. 6(6), 1273\u20131298 (2017)","journal-title":"Optim. Methods Softw."},{"key":"2153_CR13","doi-asserted-by":"crossref","unstructured":"Cartis, C., Gould, N.I.M., Toint, P.L.: Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization. In: Sirakov, B., de Souza, P., Viana, M. (eds.) Invited Lectures, Proceedings of the 2018 International Conference of Mathematicians (ICM 2018), vol. 4, pp. 3729\u20133768. World Scientific Publishing Co Pte Ltd, Rio de Janeiro (2018)","DOI":"10.1142\/9789813272880_0198"},{"issue":"1","key":"2153_CR14","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1137\/16M1106316","volume":"29","author":"C Cartis","year":"2019","unstructured":"Cartis, C., Gould, N.I.M., Toint, P.L.: Universal regularization methods-varying the power, the smoothness and the accuracy. SIAM J. Optim. 29(1), 595\u2013615 (2019)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"2153_CR15","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1137\/17M1144854","volume":"30","author":"C Cartis","year":"2020","unstructured":"Cartis, C., Gould, N.I.M., Toint, P.L.: Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints. SIAM J. Optim. 30(1), 513\u2013541 (2020)","journal-title":"SIAM J. Optim."},{"key":"2153_CR16","unstructured":"Cartis, C., Gould, N.I.M., Toint. P.L.: Strong evaluation complexity bounds for arbitrary-order optimization of nonconvex nonsmooth composite functions. arXiv:2001.10802 (2020)"},{"key":"2153_CR17","unstructured":"Cartis, C., Gould, N.I.M., Toint, P.L.: Strong evaluation complexity of an inexact trust-region algorithm for arbitrary-order unconstrained nonconvex optimization. arXiv:2011.00854 (2020)"},{"issue":"2","key":"2153_CR18","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1007\/s10107-017-1141-8","volume":"169","author":"R Chen","year":"2018","unstructured":"Chen, R., Menickelly, M., Scheinberg, K.: Stochastic optimization using a trust-region method and random models. Math. Program. Ser. A 169(2), 447\u2013487 (2018)","journal-title":"Math. Program. Ser. A"},{"key":"2153_CR19","series-title":"MPS-SIAM Series on Optimization","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719857","volume-title":"Trust-Region Methods","author":"AR Conn","year":"2000","unstructured":"Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust-Region Methods. MPS-SIAM Series on Optimization, SIAM, Philadelphia (2000)"},{"issue":"1","key":"2153_CR20","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1287\/moor.2018.0983","volume":"45","author":"E de Klerk","year":"2019","unstructured":"de Klerk, E., Laurent, M.: Worst-case examples for Lasserre\u2019s measure-based hierarchy for polynomial optimization on the hypercube. Math. Oper. Res. 45(1), 86\u201398 (2019)","journal-title":"Math. Oper. Res."},{"key":"2153_CR21","doi-asserted-by":"crossref","unstructured":"de\u00a0Klerk, E., Laurent, M.: Convergence analysis of a Lasserre hierarchy of upper bounds for polynomial minimization on the sphere. Math. Program. 1\u201321 (2020)","DOI":"10.1007\/s10107-019-01465-1"},{"issue":"1","key":"2153_CR22","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1137\/16M1087801","volume":"27","author":"GN Grapiglia","year":"2017","unstructured":"Grapiglia, G.N., Nesterov, Yu.: Regularized Newton methods for minimizing functions with H\u00f6lder continuous Hessians. SIAM J. Optim. 27(1), 478\u2013506 (2017)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"2153_CR23","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1137\/050623012","volume":"19","author":"S Gratton","year":"2008","unstructured":"Gratton, S., Sartenaer, A., Toint, P.L.: Recursive trust-region methods for multiscale nonlinear optimization. SIAM J. Optim. 19(1), 414\u2013444 (2008)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"2153_CR24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10107-020-01466-5","volume":"187","author":"S Gratton","year":"2021","unstructured":"Gratton, S., Simon, E., Toint, P.L.: An algorithm for the minimization of nonsmooth nonconvex functions using inexact evaluations and its worst-case complexity. Math. Program. Ser. A 187(1), 1\u201324 (2021)","journal-title":"Math. Program. Ser. A"},{"issue":"3","key":"2153_CR25","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1007\/s10589-020-00190-2","volume":"76","author":"S Gratton","year":"2020","unstructured":"Gratton, S., Toint, P.L.: A note on solving nonlinear optimization problems in variable precision. Comput. Optim. Appl. 76(3), 917\u2013933 (2020)","journal-title":"Comput. Optim. Appl."},{"key":"2153_CR26","unstructured":"Gratton, S., Toint, P.L.: OPM, a collection of optimization problems in Matlab. arXiv preprint arXiv:2112.05636 (2021)"},{"key":"2153_CR27","doi-asserted-by":"crossref","unstructured":"Higham, N.J.: The rise of multiprecision computations. Talk at SAMSI 2017, April (2017). https:\/\/bit.ly\/higham-samsi17","DOI":"10.1109\/ARITH.2017.24"},{"issue":"1","key":"2153_CR28","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1145\/355934.355936","volume":"7","author":"JJ Mor\u00e9","year":"1981","unstructured":"Mor\u00e9, J.J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained optimization software. ACM Trans. Math. Softw. 7(1), 17\u201341 (1981)","journal-title":"ACM Trans. Math. Softw."},{"issue":"1","key":"2153_CR29","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/s10107-012-0629-5","volume":"140","author":"Yu Nesterov","year":"2013","unstructured":"Nesterov, Yu.: Gradient methods for minimizing composite objective functions. Math. Program. Ser. A 140(1), 125\u2013161 (2013)","journal-title":"Math. Program. Ser. A"},{"issue":"1\u20132","key":"2153_CR30","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/s10107-014-0790-0","volume":"152","author":"Yu Nesterov","year":"2015","unstructured":"Nesterov, Yu.: Universal gradient methods for convex optimization problems. Math. Program. Ser. A 152(1\u20132), 381\u2013404 (2015)","journal-title":"Math. Program. Ser. A"},{"key":"2153_CR31","unstructured":"Oztoprak, F., Byrd, R., Nocedal, J.: Constrained optimization in the presence of noise. arXiv:2110.04355 (2021)"},{"issue":"1","key":"2153_CR32","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1137\/18M1216250","volume":"30","author":"C Paquette","year":"2020","unstructured":"Paquette, C., Scheinberg, K.: A stochastic line search method with convergence rate analysis. SIAM J. Optim. 30(1), 349\u2013376 (2020)","journal-title":"SIAM J. Optim."},{"key":"2153_CR33","doi-asserted-by":"crossref","unstructured":"Slot, L., Laurent, M.: Improved convergence analysis of Lasserre\u2019s measure-based upper bounds for polynomial minimization on compact sets. Math. Program. 1\u201341 (2020)","DOI":"10.1007\/s10107-020-01468-3"},{"key":"2153_CR34","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/s10107-019-01405-z","volume":"184","author":"P Xu","year":"2020","unstructured":"Xu, P., Roosta-Khorasani, F., Mahoney, M.W.: Newton-type methods for non-convex optimization under inexact Hessian information. Math. Program. Ser. A 184, 35\u201370 (2020)","journal-title":"Math. Program. Ser. A"},{"issue":"2","key":"2153_CR35","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1287\/ijoo.2019.0043","volume":"3","author":"Z Yao","year":"2021","unstructured":"Yao, Z., Xu, P., Roosta-Khorasani, F., Mahoney, M.W.: Inexact non-convex Newton-type methods. INFORMS J. Optim. 3(2), 154\u2013182 (2021)","journal-title":"INFORMS J. Optim."},{"issue":"1","key":"2153_CR36","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s10107-015-0893-2","volume":"151","author":"Y Yuan","year":"2015","unstructured":"Yuan, Y.: Recent advances in trust region algorithms. Math. Program. Ser. A 151(1), 249\u2013281 (2015)","journal-title":"Math. Program. Ser. A"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-022-02153-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-022-02153-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-022-02153-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T06:41:28Z","timestamp":1676616088000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-022-02153-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,9]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["2153"],"URL":"https:\/\/doi.org\/10.1007\/s10957-022-02153-5","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,9]]},"assertion":[{"value":"21 December 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 December 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 January 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}