Let's say we have a function $f:\Bbb R^m\to\Bbb R^n$, what does it mean for $f$ to be convex?
I stumbled upon this term in article on high dimensional probability theory and I couldn't find a reference for it.
PS. I would really appreciate if you can also point me to a nice article or paper about basic theory about multidimensional convex functions.
Even in such a general setting as functional analysis (e.g., Brezis's book), the convexity of a function is defined as the convexity, as a set, of that function's hypergraph. The definition of hypergraph, in turn, makes sense only when the function is scalar-valued.
Nevertheless, I found the following (see the very top of page 186): https://ccrma.stanford.edu/~dattorro/gcf.pdf