Abstract
Let C be a nonempty closed convex subset of \(\mathcal{H}\). The projection \( P_{c}x \)of a point \( x\, \in \, \mathcal{H} \) onto C is characterized by (see Theorem 3.14)
or, equivalently, by (see Proposition 6.46) \( x - {P_{c}x } \in N_c\left( {P_{c}x } \right)\)). In this chapter, we investigate further the properties of projectors and provide a variety of examples.
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© 2011 Springer Science+Business Media, LLC
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Bauschke, H.H., Combettes, P.L. (2011). Projection Operators. In: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9467-7_28
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DOI: https://doi.org/10.1007/978-1-4419-9467-7_28
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-9466-0
Online ISBN: 978-1-4419-9467-7
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