{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,9,23]],"date-time":"2022-09-23T12:16:43Z","timestamp":1663935403925},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,2,27]],"date-time":"2013-02-27T00:00:00Z","timestamp":1361923200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2013,9]]},"DOI":"10.1007\/s10589-013-9546-7","type":"journal-article","created":{"date-parts":[[2013,2,26]],"date-time":"2013-02-26T18:58:23Z","timestamp":1361905103000},"page":"39-61","source":"Crossref","is-referenced-by-count":8,"title":["Using inexact gradients in a multilevel optimization algorithm"],"prefix":"10.1007","volume":"56","author":[{"given":"Robert Michael","family":"Lewis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen G.","family":"Nash","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,2,27]]},"reference":[{"issue":"134","key":"9546_CR1","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1090\/S0025-5718-1976-0395209-4","volume":"30","author":"P.T. Boggs","year":"1976","unstructured":"Boggs, P.T., Dennis, J.E. Jr.: A stability analysis for perturbed nonlinear iterative methods. Math. Comput. 30(134), 199\u2013215 (1976)","journal-title":"Math. Comput."},{"key":"9546_CR2","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.1137\/110856411","volume":"22","author":"P.T. Boggs","year":"2012","unstructured":"Boggs, P.T., Gay, D.M., Griffiths, S., Lewis, R.M., Long, K.R., Nash, S., Nilson, R.H.: Optimization algorithms for hierarchical problems, with application to nanoporous materials. SIAM J. Optim. 22, 1285\u20131308 (2012)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"9546_CR3","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1137\/0728014","volume":"28","author":"R.G. Carter","year":"1991","unstructured":"Carter, R.G.: On the global convergence of trust region algorithms using inexact gradient information. SIAM J. Numer. Anal. 28(1), 251\u2013265 (1991)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"9546_CR4","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1137\/0914023","volume":"14","author":"R.G. Carter","year":"1993","unstructured":"Carter, R.G.: Numerical experience with a class of algorithms for nonlinear optimization using inexact function and gradient information. SIAM J. Sci. Comput. 14(2), 368\u2013388 (1993)","journal-title":"SIAM J. Sci. Comput."},{"key":"9546_CR5","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1093\/imanum\/drn045","volume":"28","author":"A.L. Cust\u00f3dio","year":"2008","unstructured":"Cust\u00f3dio, A.L., Dennis, J.E. Jr., Vicente, L.N.: Using simplex gradients of nonsmooth functions in direct search methods. IMA J. Numer. Anal. 28, 770\u2013784 (2008)","journal-title":"IMA J. Numer. Anal."},{"issue":"3","key":"9546_CR6","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1137\/S003614450242889","volume":"45","author":"T.G. Kolda","year":"2003","unstructured":"Kolda, T.G., Lewis, R.M., Torczon, V.: Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev. 45(3), 385\u2013482 (2003)","journal-title":"SIAM Rev."},{"key":"9546_CR7","doi-asserted-by":"crossref","first-page":"1811","DOI":"10.1137\/S1064827502407792","volume":"26","author":"R.M. Lewis","year":"2005","unstructured":"Lewis, R.M., Nash, S.G.: Model problems for the multigrid optimization of systems governed by differential equations. SIAM J. Sci. Comput. 26, 1811\u20131837 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"9546_CR8","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1007\/978-3-642-68874-4_11","volume-title":"Mathematical Programming: the State of the Art","author":"J.J. Mor\u00e9","year":"1983","unstructured":"Mor\u00e9, J.J.: Recent developments in algorithms and software for trust region methods. In: Bachem, A., Gr\u00f6tschel, M., Korte, B. (eds.) Mathematical Programming: the State of the Art, pp.\u00a0258\u2013287. Springer, Berlin (1983)"},{"key":"9546_CR9","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1080\/10556780008805795","volume":"14","author":"S.G. Nash","year":"2000","unstructured":"Nash, S.G.: A multigrid approach to discretized optimization problems. Optim. Methods Softw. 14, 99\u2013116 (2000)","journal-title":"Optim. Methods Softw."},{"key":"9546_CR10","unstructured":"Nash, S.G.: Convergence and descent properties for a class of multilevel optimization algorithms (2010). http:\/\/www.optimization-online.org\/DB_HTML\/2010\/04\/2598.html"},{"key":"9546_CR11","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1080\/10556788.2010.525637","volume":"26","author":"S.G. Nash","year":"2011","unstructured":"Nash, S.G., Lewis, R.M.: Assessing the performance of an optimization-based multilevel method. Optim. Methods Softw. 26, 693\u2013717 (2011)","journal-title":"Optim. Methods Softw."},{"key":"9546_CR12","volume-title":"Finite Difference Schemes and Partial Differential Equations","author":"J.C. Strikwerda","year":"1989","unstructured":"Strikwerda, J.C.: Finite Difference Schemes and Partial Differential Equations. Wadsworth & Brooks, Cole (1989)"},{"key":"9546_CR13","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1093\/imanum\/8.2.231","volume":"8","author":"P.L. Toint","year":"1988","unstructured":"Toint, P.L.: Global convergence of a class of trust region methods for nonconvex minimization in Hilbert space. IMA J. Numer. Anal. 8, 231\u2013252 (1988)","journal-title":"IMA J. Numer. Anal."},{"key":"9546_CR14","volume-title":"Multigrid","author":"U. Trottenberg","year":"2001","unstructured":"Trottenberg, U., Oosterlee, C., Sch\u00fcller, A.: Multigrid. Academic Press, London (2001)"}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-013-9546-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-013-9546-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-013-9546-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T18:37:34Z","timestamp":1559241454000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-013-9546-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,27]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,9]]}},"alternative-id":["9546"],"URL":"https:\/\/doi.org\/10.1007\/s10589-013-9546-7","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2,27]]}}}