Error using Mosek Solver with binary constraints

[Mark_L_Stone]

There is sort of an exception. If CVX can convert the semidefinite constraints into SOCP constraints, as for instance with any 2 by 2 semidefinite constraints, then it would pass the problem to Mosek as an MISOCP, and MOsek could solve it.

For instance,

cvx_begin
cvx_solver mosek
variable X(2,2) integer symmetric
;minimize(trace(X))
X >=2
X==semidefinite(2)
cvx_end

CVX 2.2 disallows declaration of semidefinite and (integer or binary).

Here is an old post on the subject from the CVX developer

Mixed Integer SDPs which are not Mixed Integer SOCPs

I do not think I can be quite categorical about this. CVX will indeed convert all 2x2 LMIs into SOC equivalents (both real and complex). And CVX does not use 3x3-or-larger LMIs unless it has to. But if you force the issue by specifying, say, an arrow-shaped 4x4 LMI, CVX will not detect that.