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Restricted Normal Cones and the Method of Alternating Projections: Theory

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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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Authors and Affiliations

  1. Mathematics, University of British Columbia, Kelowna, BC, V1V 1V7, Canada

    Heinz H. Bauschke & Xianfu Wang

  2. Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Lotzestr. 16–18, 37083, Göttingen, Germany

    D. Russell Luke

  3. Department of Mathematics & Statistics, University of Victoria, PO Box 3060 STN CSC, Victoria, BC, V8W 3R4, Canada

    Hung M. Phan

Authors
  1. Heinz H. Bauschke
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  2. D. Russell Luke
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  3. Hung M. Phan
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  4. Xianfu Wang
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Correspondence to Heinz H. Bauschke.

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Bauschke, H.H., Luke, D.R., Phan, H.M. et al. Restricted Normal Cones and the Method of Alternating Projections: Theory. Set-Valued Var. Anal 21, 431–473 (2013). https://doi.org/10.1007/s11228-013-0239-2

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