Gauge function

From Glossary

Jump to: navigation, search

A nonnegative, convex function, from LaTeX: \mathbb{R}^n to the extended reals that is positively homogeneous and LaTeX: f(0)=0. A norm is a gauge function. Here is an example that is not a norm:

f(x,y,z) = \left\{ \begin{array}{rl}
<pre>          \| (x-z,\; x-y) \|_2, & 2x - y - z = 0 \\ \\
          \infty, & \mbox{ otherwise.}
          \end{array} \right.

Personal tools