Abstract
Source conditions of the type
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: HO 1454/10-1
Funding statement: Research supported by Deutsche Forschungsgemeinschaft (DFG-grant HO 1454/10-1).
Acknowledgements
The author thanks the anonymous referees for their comments that helped to improve this paper. The helpful comments and discussions with Bernd Hofmann (TU Chemnitz) and Oliver Ernst (TU Chemnitz) are gratefully acknowledged.
References
[1] J. Bolte, A. Daniilidis and A. Lewis, The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems, SIAM J. Optim. 17 (2006), no. 4, 1205–1223. 10.1137/050644641Search in Google Scholar
[2] J. Bolte, A. Daniilidis, A. Lewis and M. Shiota, Clarke subgradients of stratifiable functions, SIAM J. Optim. 18 (2007), no. 2, 556–572. 10.1137/060670080Search in Google Scholar
[3] J. Bolte, A. Daniilidis, O. Ley and L. Mazet, Characterizations of Ł ojasiewicz inequalities: Subgradient flows, talweg, convexity, Trans. Amer. Math. Soc. 362 (2010), no. 6, 3319–3363. 10.1090/S0002-9947-09-05048-XSearch in Google Scholar
[4] J. Bolte, S. Sabach and M. Teboulle, Proximal alternating linearized minimization for nonconvex and nonsmooth problems, Math. Program. 146 (2014), no. 1–2, 459–494. 10.1007/s10107-013-0701-9Search in Google Scholar
[5] T. Bubba, A. Hauptmann, S. Houtari, J. Rimpeläinen and S. Siltanen, Tomographic X-ray data of a lotus root slice filled with different chemical elements, preprint (2016), http://arxiv.org/abs/1609.07299. Search in Google Scholar
[6] T. Bubba, M. Juvonen, J. Lehtonen, M. März, A. Meaney, Z. Purisha and S. Siltanen, Tomographic X-ray data of carved cheese, preprint (2017), http://arxiv.org/abs/1705.05732. Search in Google Scholar
[7] H. W. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems, Math. Appl. 375, Kluwer Academic, Dordrecht, 1996. 10.1007/978-94-009-1740-8Search in Google Scholar
[8] K. Hämäläinen, L. Harhanen, A. Kallonen, A. Kujunpää, E. Niemi and S. Siltanen, Tomographic X-ray data of a walnut, preprint (2015), http://arxiv.org/abs/1502.04064. Search in Google Scholar
[9] P. C. Hansen, Regularization Tools version 4.0 for Matlab 7.3, Numer. Algorithms 46 (2007), no. 2, 189–194. 10.1007/s11075-007-9136-9Search in Google Scholar
[10] K. Kurdyka, On gradients of functions definable in o-minimal structures, Ann. Inst. Fourier (Grenoble) 48 (1998), no. 3, 769–783. 10.5802/aif.1638Search in Google Scholar
[11] S. Łojasiewicz, Une propriété topologique des sous-ensembles analytiques réels, Les Équations aux Dérivées Partielles (Paris 1962), Éditions du Centre National de la Recherche Scientifique, Paris (1963), 87–89. Search in Google Scholar
[12] S. Łojasiewicz, Ensembles semi-analytiques, Lecture notes, Institut des Hautes Etudes Scientifiques Bures-sur-Yvette (Seine-et-Oise), France, 1965, http://perso.univ-rennes1.fr/michel.coste/Lojasiewicz.pdf. Search in Google Scholar
[13] A. K. Louis, Inverse und schlecht gestellte Probleme, Teubner Studienbücher Math., B. G. Teubner, Stuttgart, 1989. 10.1007/978-3-322-84808-6Search in Google Scholar
[14] V. A. Morozov, On the solution of functional equations by the method of regularization, Soviet Math. Dokl. 7 (1966), 414–417. Search in Google Scholar
[15] J. Shao, Mathematical Statistics, 2nd ed., Springer Texts Statist., Springer, New York, 2003. 10.1007/b97553Search in Google Scholar
[16] A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-posed Problems, V. H. Winston & Sons, Washington, 1977. Search in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
