- E3
[0ZX] Let \(X\) be a vector space and \(f:V→ {\mathbb {R}}\) a function that is positively homogeneous, that is: for every \(v∈ X\) and \(t≥ 0\) you have \(t f(v)=f (tv)\).
Show that \(f\) is convex if and only if the triangle inequality holds: for every \(v,w∈ X\) you have
\[ f(v+w) ≤ f(v)+f(w)\quad . \]In particular, a norm is always a convex function.
EDB — 0ZX
View
English
Authors:
"Mennucci , Andrea C. G."
.
Bibliography
Book index
Book index
- normed vector space
- function, positively homogeneous
- triangle inequality
- convex function
Managing blob in: Multiple languages