  Gauge functions significantly generalize the notion of a norm, and gauge
optimization, as defined by Freund (1987}, seeks the element of a convex set
that is minimal with respect to a gauge function. This conceptually simple
problem can be used to model a remarkable array of useful problems, including a
special case of conic optimization, and related problems that arise in machine
learning and signal processing. The gauge structure of these problems allows
for a special kind of duality framework. This paper explores the duality
framework proposed by Freund, and proposes a particular form of the problem
that exposes some useful properties of the gauge optimization framework (such
as the variational properties of its value function), and yet maintains most of
the generality of the abstract form of gauge optimization.
