This question pertains to the Conic Benchmark Format (CBF) for specifying a convex optimization problem. Here's a link to the specification.

In the CBF specification, there are separate areas for positive semidefinite (psd) constraints and psd variables. But why should there be two separate areas? This seems completely redundant. No other convex cone is treated separately like this--variables are declared and then later constrained to be in a specific cone.

Are there any benefits (other than a shortcut for declaring variables subject to a psd constraint) that justify why the PSDVAR section should exist? I'm thinking specifically about benefits to the solver. Could any solvers be expected to take advantage of the fact that a variable was declared psd instead of a symmetric matrix later being constrained psd?