  In many applications, solutions of convex optimization problems are updated
on-line, as functions of time. In this paper, we consider parametric
semidefinite programs, which are linear optimization problems in the
semidefinite cone whose coefficients (input data) depend on a time parameter.
We are interested in the geometry of the solution (output data) trajectory,
defined as the set of solutions depending on the parameter. We propose an
exhaustive description of the geometry of the solution trajectory. As our main
result, we show that only six distinct behaviors can be observed at a
neighborhood of a given point along the solution trajectory. Each possible
behavior is then illustrated by an example.
