Restricted Normal Cones and the Method of Alternating Projections: Theory

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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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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Keywords

  • Constraint qualification
  • Convex set
  • Friedrichs angle
  • Normal cone
  • Nonconvex set
  • Projection operator
  • Restricted normal cone
  • Superregularity

Mathematics Subject Classifications (2010)

  • Primary 49J52; Secondary 47H09
  • 90C26