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Restricted Normal Cones and the Method of Alternating Projections: Theory |
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| Authors: | Heinz H. Bauschke D. Russell Luke Hung M. Phan Xianfu Wang |
| Affiliation: | 1. Mathematics, University of British Columbia, Kelowna, BC, V1V?1V7, Canada 2. Institut für Numerische und Angewandte Mathematik, Universit?t G?ttingen, Lotzestr.?16–18, 37083, G?ttingen, Germany 3. Department of Mathematics & Statistics, University of Victoria, PO Box 3060 STN CSC, Victoria, BC, V8W?3R4, Canada |
| Abstract: | In this paper, we introduce and develop the theory of restricted normal cones which generalize the classical Mordukhovich normal cone. We thoroughly study these objects from the viewpoint of constraint qualifications and regularity. Numerous examples are provided to illustrate the theory. This work provides the theoretical underpinning for a subsequent article in which these tools are applied to obtain a convergence analysis of the method of alternating projections for nonconvex sets. |
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