what does projection $\pi$ mean?

Question

I am reading a paper where I encountered the following -

\begin{equation} Z(x) = \pi_{[-c,c]^{n}} (\nabla F(x)-x) \end{equation}

what does the first term mean? Its mentioned in the paper that $\pi_{[-c,c]^{n}} (q)$ is projection and it acts components wise on q - Which I cannot understand. Can someone elaborate on it?

Answer 1

Let me try my shot at it. I believe x is a vector, e.g. grad of F(x) = <Fx1, Fx2>

q = <Fx1, Fx2> - <x1, x2>

q = (Fx1 - x1)i + (Fx2 - x2)j

q is a vector of component i & j.