  In many applications, solutions of convex optimization problems must be
updated on-line, as functions of time. In this paper, we consider time-varying
semidefinite programs (TV-SDP), which are linear optimization problems in the
semidefinite cone whose coefficients (input data) depend on time. We are
interested in the geometry of the solution (output data) trajectory, defined as
the set of solutions depending on time. We propose an exhaustive description of
the geometry of the solution trajectory. As our main result, we show that only
6 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.
