Ill-Posedness of sublinear minimization problems
It is well known that minimization problems involving sublinear regularization terms are ill-posed, in Sobolev spaces. Extended results to spaces of bounded variation functions BV were recently showed in the special case of bounded regularization terms. In this note, a generalization to sublinear re...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2011-04-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110256X11000071 |
| _version_ | 1818279630020280320 |
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| author | S. Issa M. Jazar A. El Hamidi |
| author_facet | S. Issa M. Jazar A. El Hamidi |
| author_sort | S. Issa |
| collection | DOAJ |
| description | It is well known that minimization problems involving sublinear regularization terms are ill-posed, in Sobolev spaces. Extended results to spaces of bounded variation functions BV were recently showed in the special case of bounded regularization terms. In this note, a generalization to sublinear regularization is presented in BV spaces. Notice that our results are optimal in the sense that linear regularization leads to well-posed minimization problems in BV spaces. |
| first_indexed | 2024-12-12T23:36:23Z |
| format | Article |
| id | doaj.art-937a539da97040e4828389a3e770abc4 |
| institution | Directory Open Access Journal |
| issn | 1110-256X |
| language | English |
| last_indexed | 2024-12-12T23:36:23Z |
| publishDate | 2011-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-937a539da97040e4828389a3e770abc42022-12-22T00:07:26ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2011-04-01191889010.1016/j.joems.2011.09.004Ill-Posedness of sublinear minimization problemsS. Issa0M. Jazar1A. El Hamidi2LaMA-Liban, Azm Research Center, EDST, Lebanese University, Tripoli, LebanonLaMA-Liban, Azm Research Center, EDST, Lebanese University, Tripoli, LebanonLMA, Université de La Rochelle, FranceIt is well known that minimization problems involving sublinear regularization terms are ill-posed, in Sobolev spaces. Extended results to spaces of bounded variation functions BV were recently showed in the special case of bounded regularization terms. In this note, a generalization to sublinear regularization is presented in BV spaces. Notice that our results are optimal in the sense that linear regularization leads to well-posed minimization problems in BV spaces.http://www.sciencedirect.com/science/article/pii/S1110256X11000071Bounded variationNonconvex regularizationChambolle’s projectionTexture |
| spellingShingle | S. Issa M. Jazar A. El Hamidi Ill-Posedness of sublinear minimization problems Journal of the Egyptian Mathematical Society Bounded variation Nonconvex regularization Chambolle’s projection Texture |
| title | Ill-Posedness of sublinear minimization problems |
| title_full | Ill-Posedness of sublinear minimization problems |
| title_fullStr | Ill-Posedness of sublinear minimization problems |
| title_full_unstemmed | Ill-Posedness of sublinear minimization problems |
| title_short | Ill-Posedness of sublinear minimization problems |
| title_sort | ill posedness of sublinear minimization problems |
| topic | Bounded variation Nonconvex regularization Chambolle’s projection Texture |
| url | http://www.sciencedirect.com/science/article/pii/S1110256X11000071 |
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