{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T06:04:44Z","timestamp":1780553084076,"version":"3.54.1"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2015,9,8]],"date-time":"2015-09-08T00:00:00Z","timestamp":1441670400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2016,8]]},"DOI":"10.1007\/s00211-015-0764-z","type":"journal-article","created":{"date-parts":[[2015,9,8]],"date-time":"2015-09-08T12:00:47Z","timestamp":1441713647000},"page":"655-684","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Levenberg\u2013Marquardt method in Banach spaces with general convex regularization terms"],"prefix":"10.1007","volume":"133","author":[{"given":"Qinian","family":"Jin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongqi","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2015,9,8]]},"reference":[{"issue":"10","key":"764_CR1","doi-asserted-by":"crossref","first-page":"105004","DOI":"10.1088\/0266-5611\/25\/10\/105004","volume":"25","author":"M Bachmayr","year":"2009","unstructured":"Bachmayr, M., Burger, M.: Iterative total variation schemes for nonlinear inverse problems. Inverse Probl. 25(10), 105004 (2009)","journal-title":"Inverse Probl."},{"key":"764_CR2","doi-asserted-by":"crossref","unstructured":"Bakushinsky, A.B., Kokurin, M.Y.: Iterative Methods for Approximate Solutions of Inverse Problems. Mathematics and Its Applications (New York), vol. 577. Springer, Dordrecht (2004)","DOI":"10.1007\/978-1-4020-3122-9"},{"key":"764_CR3","doi-asserted-by":"crossref","DOI":"10.1002\/0471787779","volume-title":"Nonlinear Programming, Theory and Algorithms, 3rd edn","author":"MS Bazaraa","year":"2006","unstructured":"Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming, Theory and Algorithms, 3rd edn. Wiley-Interscience, New York (2006)"},{"key":"764_CR4","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/080716542","volume":"2","author":"A Beck","year":"2009","unstructured":"Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2, 183\u2013202 (2009)","journal-title":"SIAM J. Imaging Sci."},{"key":"764_CR5","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1007\/s10851-010-0251-1","volume":"40","author":"A Chambolle","year":"2011","unstructured":"Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40, 120\u2013145 (2011)","journal-title":"J. Math. Imaging Vis."},{"key":"764_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-2121-4","volume-title":"Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems","author":"I Cioranescu","year":"1990","unstructured":"Cioranescu, I.: Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems. Kluwer, Dordrecht (1990)"},{"key":"764_CR7","first-page":"1","volume":"370","author":"F Colonius","year":"1986","unstructured":"Colonius, F., Kunisch, K.: Stability for parameter estimation in two point boundary value problems. J. Reine Angew. Math. 370, 1\u201329 (1986)","journal-title":"J. Reine Angew. Math."},{"key":"764_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-1740-8","volume-title":"Regularization of Inverse Problems","author":"HW Engl","year":"1996","unstructured":"Engl, H.W., Hanke, M., Neunauer, A.: Regularization of Inverse Problems. Kluwer, Dordrecht (1996)"},{"key":"764_CR9","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1088\/0266-5611\/5\/4\/007","volume":"5","author":"HW Engl","year":"1989","unstructured":"Engl, H.W., Kunisch, K., Neubauer, A.: Convergence rates of Tikhonov regularization of nonlinear ill-posed problems. Inverse Probl. 5, 523\u2013540 (1989)","journal-title":"Inverse Probl."},{"issue":"9\u201310","key":"764_CR10","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1080\/01630569708816804","volume":"18","author":"M Hanke","year":"1997","unstructured":"Hanke, M.: Regularizing properties of a truncated Newton-CG algorithm for nonlinear inverse problems. Numer. Funct. Anal. Optim. 18(9\u201310), 971\u2013993 (1997)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"764_CR11","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1088\/0266-5611\/13\/1\/007","volume":"13","author":"M Hanke","year":"1997","unstructured":"Hanke, M.: A regularizing Levenberg\u2013Marquardt scheme with applications to inverse groundwater filtration problems. Inverse Probl. 13, 79\u201395 (1997)","journal-title":"Inverse Probl."},{"key":"764_CR12","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s002110050158","volume":"72","author":"M Hanke","year":"1995","unstructured":"Hanke, M., Neubauer, A., Scherzer, O.: A convergence analysis of the Landweber iteration for nonlinear ill-posed problems. Numer. Math. 72, 21\u201337 (1995)","journal-title":"Numer. Math."},{"issue":"2","key":"764_CR13","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1137\/S0036142998341246","volume":"37","author":"F Hettlich","year":"2000","unstructured":"Hettlich, F., Rundell, W.: A second degree method for nonlinear inverse problems. SIAM J. Numer. Anal. 37(2), 587\u2013620 (2000)","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"764_CR14","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1007\/s00211-012-0499-z","volume":"123","author":"T Hohage","year":"2013","unstructured":"Hohage, T., Werner, F.: Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data. Numer. Math. 123(4), 745\u2013779 (2013)","journal-title":"Numer. Math."},{"key":"764_CR15","doi-asserted-by":"crossref","unstructured":"Hohage, T., Werner, F.: Convergence rates for inverse problems with impulsive noise. SIAM J. Numer. Anal. 52(3), 1203\u20131221 (2014)","DOI":"10.1137\/130932661"},{"issue":"2","key":"764_CR16","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1137\/S0036142997315470","volume":"36","author":"Q Jin","year":"1999","unstructured":"Jin, Q.: Applications of the modified discrepancy principle to Tikhonov regularization of nonlinear ill-posed problems. SIAM J. Numer. Anal. 36(2), 475\u2013490 (1999)","journal-title":"SIAM J. Numer. Anal."},{"key":"764_CR17","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/s00211-011-0435-7","volume":"121","author":"Q Jin","year":"2012","unstructured":"Jin, Q.: On the order optimality of the regularization via inexact Newton iterations. Numer. Math. 121, 237\u2013260 (2012)","journal-title":"Numer. Math."},{"key":"764_CR18","doi-asserted-by":"crossref","unstructured":"Jin, Q.: Inexact Newton\u2013Landweber iteration for solving nonlinear inverse problems in Banach spaces. Inverse Probl. 28, 065002 (15pp) (2012)","DOI":"10.1088\/0266-5611\/28\/6\/065002"},{"key":"764_CR19","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1007\/s00211-008-0198-y","volume":"111","author":"Q Jin","year":"2009","unstructured":"Jin, Q., Tautenhahn, U.: On the discrepancy principle for some Newton type methods for solving nonlinear inverse problems. Numer. Math. 111, 509\u2013558 (2009)","journal-title":"Numer. Math."},{"key":"764_CR20","doi-asserted-by":"crossref","unstructured":"Jin, Q., Wang, W.: Landweber iteration of Kaczmarz type with general non-smooth convex penalty functionals. Inverse Probl. 29, 085011 (22pp) (2013)","DOI":"10.1088\/0266-5611\/29\/8\/085011"},{"key":"764_CR21","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1007\/s00211-013-0529-5","volume":"124","author":"Q Jin","year":"2013","unstructured":"Jin, Q., Zhong, M.: On the iteratively regularized Gauss\u2013Newton method in Banach spaces with applications to parameter identification problems. Numer. Math. 124, 647\u2013683 (2013)","journal-title":"Numer. Math."},{"key":"764_CR22","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1007\/s00211-013-0594-9","volume":"127","author":"Q Jin","year":"2014","unstructured":"Jin, Q., Zhong, M.: Nonstationary iterated Tikhonov regularization in Banach spaces with uniformly convex penalty terms. Numer. Math. 127, 485\u2013513 (2014)","journal-title":"Numer. Math."},{"key":"764_CR23","doi-asserted-by":"crossref","unstructured":"Kaltenbacher, B.: A convergence rates result for an iteratively regularized Gauss\u2013Newton\u2013Halley method in Banach space. Inverse Probl. 31, 015007 (20pp) (2015)","DOI":"10.1088\/0266-5611\/31\/1\/015007"},{"key":"764_CR24","doi-asserted-by":"crossref","unstructured":"Kaltenbacher, B., Hofmann, B.: Convergence rates for the iteratively regularized Gauss\u2013Newton method in Banach spaces. Inverse Probl. 26, 035007 (21pp) (2010)","DOI":"10.1088\/0266-5611\/26\/3\/035007"},{"key":"764_CR25","doi-asserted-by":"crossref","DOI":"10.1515\/9783110208276","volume-title":"Iterative Regularization Methods for Nonlinear Ill-Posed Problems","author":"B Kaltenbacher","year":"2008","unstructured":"Kaltenbacher, B., Neubauer, A., Scherzer, O.: Iterative Regularization Methods for Nonlinear Ill-Posed Problems. de Gruyter, Berlin (2008)"},{"key":"764_CR26","doi-asserted-by":"crossref","unstructured":"Kaltenbacher, B., Sch\u00f6pfer, F., Schuster, T.: Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems. Inverse Probl. 25, 065003 (19pp) (2009)","DOI":"10.1088\/0266-5611\/25\/6\/065003"},{"key":"764_CR27","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1007\/s00211-009-0256-0","volume":"114","author":"A Lechleiter","year":"2010","unstructured":"Lechleiter, A., Rieder, A.: Towards a general convergence theory for inexact Newton regularizations. Numer. Math. 114, 521\u2013548 (2010)","journal-title":"Numer. Math."},{"key":"764_CR28","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1137\/130923956","volume":"52","author":"F Margotti","year":"2014","unstructured":"Margotti, F., Rieder, A., Leit\u00e4o, A.: A Kaczmarz version of the REGINN-Landweber iteration for ill-posed problems in Banach spaces. SIAM J. Numer. Anal. 52, 1439\u20131465 (2014)","journal-title":"SIAM J. Numer. Anal."},{"key":"764_CR29","volume-title":"Numerical Optimization","author":"J Nocedal","year":"2006","unstructured":"Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, New York (2006)","edition":"2"},{"key":"764_CR30","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1088\/0266-5611\/15\/1\/028","volume":"15","author":"A Rieder","year":"1999","unstructured":"Rieder, A.: On the regularization of nonlinear ill-posed problems via inexact Newton iterations. Inverse Probl. 15, 309\u2013327 (1999)","journal-title":"Inverse Probl."},{"key":"764_CR31","doi-asserted-by":"crossref","DOI":"10.1515\/9783110255720","volume-title":"Regularization Methods in Banach Spaces","author":"T Schuster","year":"2012","unstructured":"Schuster, T., Kaltenbacher, B., Hofmann, B., Kazimierski, K.S.: Regularization Methods in Banach Spaces. Walter de Gruyter, Berlin (2012)"},{"key":"764_CR32","unstructured":"Z $$\\breve{\\text{ a }}$$ a \u02d8 linscu, C.: Convex Analysis in General Vector Spaces. World Scientific Publishing Co., Inc., River Edge (2002)"},{"key":"764_CR33","unstructured":"Zhu, M., Chan, T.F.: An efficient primaldual hybrid gradient algorithm for total variation image restoration. CAM Report 08-34, UCLA (2008)"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-015-0764-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-015-0764-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-015-0764-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,30]],"date-time":"2019-08-30T04:15:11Z","timestamp":1567138511000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-015-0764-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,8]]},"references-count":33,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,8]]}},"alternative-id":["764"],"URL":"https:\/\/doi.org\/10.1007\/s00211-015-0764-z","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9,8]]}}}