I am not sure if my code is correct although it can run without errors.

If I have the following SDP problem:

I can rewrite the above as the following:

where

And its dual problem is:

The primal problem can be solved by cvx as following:

cvx_begin sdp

variable X(3,3) symmetric;

X == semidefinite(3)

minimize(C( : )’*X( : )); \ \ inner product of matrices

subject to

A1( : )’*X( : ) == 0;

A2( : )’*X( : ) == 1;

cvx_end

Now, I am not pretty much sure if the dual of it is correct:

cvx_begin sdp

variable X(3,3) symmetric;

dual variables y1 y2

X == semidefinite(3)

minimize(C( : )’*X( : ));

subject to

y1: A1( : )’*X( : ) == 0;

y2: A2( : )’*X( : ) == 1;

cvx_end

Since there are two equality constraints, I am not sure if the dual part in the code is correct.