{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T11:52:45Z","timestamp":1759837965249},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2017,6,7]],"date-time":"2017-06-07T00:00:00Z","timestamp":1496793600000},"content-version":"unspecified","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":[[2017,12]]},"DOI":"10.1007\/s00211-017-0893-7","type":"journal-article","created":{"date-parts":[[2017,6,7]],"date-time":"2017-06-07T19:22:45Z","timestamp":1496863365000},"page":"895-922","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["A conjugate gradient like method for p-norm minimization in functional spaces"],"prefix":"10.1007","volume":"137","author":[{"given":"Claudio","family":"Estatico","sequence":"first","affiliation":[]},{"given":"Serge","family":"Gratton","sequence":"additional","affiliation":[]},{"given":"Flavia","family":"Lenti","sequence":"additional","affiliation":[]},{"given":"David","family":"Titley-Peloquin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,6,7]]},"reference":[{"key":"893_CR1","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1090\/S0002-9904-1967-11678-1","volume":"73","author":"E Asplund","year":"1967","unstructured":"Asplund, E.: Positivity of duality mappings. Bull. Am. Math. Soc. 73, 200\u2013203 (1967)","journal-title":"Bull. Am. Math. Soc."},{"key":"893_CR2","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1887\/0750304359","volume-title":"Introduction to Inverse Problems in Imaging","author":"M Bertero","year":"1998","unstructured":"Bertero, M., Boccacci, P.: Introduction to Inverse Problems in Imaging, pp. 98\u2013127. IOP Publishing, London (1998)"},{"key":"893_CR3","unstructured":"Bonesky, K., Kazimiersky, K., Maass, P., Sch\u00f6pfer, F., Schuster, T.: Minimization of Tikhonov functional in Banach spaces. Abstr. Appl. Anal. 2008, 1\u201320 (2008)"},{"key":"893_CR4","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/0041-5553(67)90040-7","volume":"7","author":"LM Bregman","year":"1967","unstructured":"Bregman, L.M.: The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming. USSR Comput. Math. Math. Phys. 7, 200\u2013217 (1967)","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"893_CR5","doi-asserted-by":"crossref","first-page":"1411","DOI":"10.1088\/0266-5611\/20\/5\/005","volume":"20","author":"M Burger","year":"2004","unstructured":"Burger, M., Osher, S.: Convergence rates of convex variational regularization. Inverse Probl. 20, 1411\u20131421 (2004)","journal-title":"Inverse Probl."},{"key":"893_CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/AAA\/2006\/84919","volume":"2006","author":"D Butnariu","year":"2006","unstructured":"Butnariu, D., Resmerita, E.: Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces. Abstr. Appl. Anal. 2006, 1\u201339 (2006)","journal-title":"Abstr. Appl. Anal."},{"key":"893_CR7","doi-asserted-by":"crossref","unstructured":"Cioranescu, I.: Geometry of Banach spaces, duality mappings and nonlinear problems. In: Hazewind, M. (ed.) Mathematics and its Applications, vol. 62, pp. 1\u201387. Kluwer Academic Publishers, Dordrecht (1990)","DOI":"10.1007\/978-94-009-2121-4"},{"key":"893_CR8","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1002\/cpa.20042","volume":"57","author":"L Daubachies","year":"2004","unstructured":"Daubachies, L., Defrise, M., De Mol, C.: An iterative thresholding algorithm for linear inverse problems with sparsity constraint. Commun. Pure Appl. Math. 57, 1413\u20131457 (2004)","journal-title":"Commun. Pure Appl. Math."},{"key":"893_CR9","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s10589-012-9527-2","volume":"54","author":"P Brianzi","year":"2013","unstructured":"Brianzi, P., Di Benedetto, F., Estatico, C.: Preconditioned iterative regularization in Banach spaces. Comput. Optim. Appl. 54, 263\u2013282 (2013)","journal-title":"Comput. Optim. Appl."},{"key":"893_CR10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0266-5611\/26\/11\/115014","volume":"26","author":"M Grasmair","year":"2010","unstructured":"Grasmair, M.: Generalized Bregman distances and convergences rate for non-convex regularization methods. Inverse Probl. 26, 1\u201320 (2010)","journal-title":"Inverse Probl."},{"key":"893_CR11","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1080\/10556788.2010.549231","volume":"26","author":"S Gratton","year":"2011","unstructured":"Gratton, S., Toint, P.L., Tr\u00f6ltzsch, A.: An active-set trust-region method for derivative-free nonlinear bound-constrained optimization. Optim. Methods Softw. 26, 873\u2013894 (2011)","journal-title":"Optim. Methods Softw."},{"key":"893_CR12","doi-asserted-by":"crossref","unstructured":"Hansen, P.C.: Rank-deficient and discrete ill-posed problem: numerical aspects of linear inversions. SIAM, Philadelphia (1998)","DOI":"10.1137\/1.9780898719697"},{"key":"893_CR13","doi-asserted-by":"publisher","unstructured":"Herzog, R., Wollner, W.: A conjugate direction method for linear systems in Banach spaces. J. Inverse Ill Posed Probl. (2016). doi: 10.1515\/jiip-2016-0027","DOI":"10.1515\/jiip-2016-0027"},{"key":"893_CR14","first-page":"53","volume":"27","author":"BT Kien","year":"2002","unstructured":"Kien, B.T.: The normalized duality mapping and two related characteristic properties of a uniformly convex Banach space. Acta Math. Vietnam. 27, 53\u201367 (2002)","journal-title":"Acta Math. Vietnam."},{"key":"893_CR15","doi-asserted-by":"crossref","first-page":"4876","DOI":"10.1109\/TGRS.2015.2411854","volume":"53","author":"F Lenti","year":"2015","unstructured":"Lenti, F., Nunziata, F., Estatico, C., Migliaccio, M.: Analysis of reconstructions obtained solving $$l^p$$ l p -penalized minimization problems. IEEE Trans. Geosci. Remote Sens. 53, 4876\u20134886 (2015)","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"893_CR16","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1109\/TGRS.2015.2458014","volume":"54","author":"F Lenti","year":"2016","unstructured":"Lenti, F., Nunziata, F., Estatico, C., Migliaccio, M.: Conjugate gradient method in Hilbert and Banach spaces to enhance the spatial resolution of radiometer data. IEEE Trans. Geosci. Remote Sens. 54, 397\u2013406 (2016)","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"893_CR17","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/978-3-662-53294-2_8","volume-title":"Classical Banach Spaces","author":"J Lindestrauss","year":"1996","unstructured":"Lindestrauss, J., Tzafriri, L.: Classical Banach Spaces, pp. 53\u2013104. Springer, Berlin (1996)"},{"key":"893_CR18","first-page":"1","volume":"3","author":"PM Milicic","year":"2002","unstructured":"Milicic, P.M.: On moduli of expansion of the duality mapping of smooth Banach spaces. J. Inequal. Pure Appl. Math. 3, 1\u20137 (2002)","journal-title":"J. Inequal. Pure Appl. Math."},{"key":"893_CR19","doi-asserted-by":"crossref","first-page":"1303","DOI":"10.1088\/0266-5611\/21\/4\/007","volume":"21","author":"E Resmerita","year":"2005","unstructured":"Resmerita, E.: Regularization of ill-posed problems in Banach spaces: convergence rates. Inverse Probl. 21, 1303\u20131314 (2005)","journal-title":"Inverse Probl."},{"key":"893_CR20","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1088\/0266-5611\/22\/1\/017","volume":"22","author":"F Sch\u00f6pfer","year":"2006","unstructured":"Sch\u00f6pfer, F., Louis, A.K., Schuster, T.: Nonlinear iterative methods for linear ill-posed problems in Banach spaces. Inverse Probl. 22, 311\u2013329 (2006)","journal-title":"Inverse Probl."},{"key":"893_CR21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0266-5611\/25\/1\/015013","volume":"25","author":"F Sch\u00f6pfer","year":"2009","unstructured":"Sch\u00f6pfer, F., Schuster, T.: Fast regularizing sequential subspace optimization in Banach spaces. Inverse Probl. 25, 1\u201322 (2009)","journal-title":"Inverse Probl."},{"key":"893_CR22","first-page":"479","volume":"15","author":"F Sch\u00f6pfer","year":"2007","unstructured":"Sch\u00f6pfer, F., Schuster, T., Louis, A.K.: Metric and Bregman projections onto affine subspaces and their computation via sequential subspace optimization methods. J. Inverse Ill Posed Probl. 15, 479\u2013506 (2007)","journal-title":"J. Inverse Ill Posed Probl."},{"key":"893_CR23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0266-5611\/24\/5\/055008","volume":"24","author":"F Sch\u00f6pfer","year":"2008","unstructured":"Sch\u00f6pfer, F., Schuster, T., Louis, A.K.: An iterative regularization method for the solution of the split feasibility problem in Banach spaces. Inverse Probl. 24, 1\u201320 (2008)","journal-title":"Inverse Probl."},{"key":"893_CR24","unstructured":"Scheinberg, K., Toint, Ph.L.: Self-correcting geometry in model based algorithms for derivative-free unconstrained optimization. Technical report, TR09\/06, Department of Mathematics University of Namur, Belgium (2009)"},{"key":"893_CR25","doi-asserted-by":"crossref","unstructured":"Schuster, T., Kaltenbacher, B., Hofmann, B., Kazimierski, K.: Regularization methods in Banach spaces. In: de Gruyter, W. (ed.) Radon Series on Computational and Applied Mathematics, vol. 10. de Gruyter, Berlin (2012)","DOI":"10.1515\/9783110255720"},{"key":"893_CR26","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0022-247X(91)90144-O","volume":"157","author":"ZB Xu","year":"1991","unstructured":"Xu, Z.B., Roach, G.F.: Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces. J. Math. Anal. Appl. 157, 189\u2013210 (1991)","journal-title":"J. Math. Anal. Appl."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-017-0893-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-017-0893-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-017-0893-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T07:39:05Z","timestamp":1659080345000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-017-0893-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,7]]},"references-count":26,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["893"],"URL":"https:\/\/doi.org\/10.1007\/s00211-017-0893-7","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,6,7]]}}}