We know a map $ T: \mathbb{R}^n \to \mathbb{R} $ is monotone if $ \forall \; x, y \in \mathbb{R}^n $, $ \; (T(x)-T(y))^T(x-y) \geq 0 $. How can we show that projection onto a convex set is a monotone map? Thank you!
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See the book "Convex Analysis and Monotone Operator Theory in Hilbert Spaces" (Bauschke and Combettes) that you can find online at http://www.ann.jussieu.fr/~plc/livre1.pdf – Jean Marie Mar 17 '16 at 12:02