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Contribution Details
| Type | Journal Article |
| Scope | Discipline-based scholarship |
| Title | Optimization methods and stability of inclusions in Banach Spaces |
| Organization Unit | |
| Authors |
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| Item Subtype | Original Work |
| Refereed | Yes |
| Status | Published in final form |
| Language |
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| Journal Title | Mathematical Programming |
| Publisher | Springer |
| Geographical Reach | international |
| ISSN | 0025-5610 |
| Volume | 117 |
| Number | 1-2 |
| Page Range | 305 - 330 |
| Date | 2009 |
| Abstract Text | Our paper deals with the interrelation of optimization methods and Lipschitz stability of multifunctions in arbitrary Banach spaces. Roughly speaking, we show that linear convergence of several first order methods and Lipschitz stability mean the same. Particularly, we characterize calmness and the Aubin property by uniformly (with respect to certain starting points) linear convergence of descent methods and approximate projection methods. So we obtain, e.g., solution methods (for solving equations or variational problems) which require calmness only. The relations of these methods to several known basic algorithms are discussed, and errors in the subroutines as well as deformations of the given mappings are permitted. We also recall how such deformations are related to standard algorithms like barrier, penalty or regularization methods in optimization. |
| Related URLs | |
| Digital Object Identifier | 10.1007/s10107-007-0174-9 |
| Other Identification Number | merlin-id:885 |
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| Additional Information | The original publication is available at www.springerlink.com. It was published electronically in 2007. |