Hello,
Looking in some examples provided with TFOCS (solved first with CVX) as “test_psdCompletion.m”, I do not understand why if you are solving the following problem:
minimize (1/2)*norm( A * X - b )^2
st X >= 0
trace(X) <= lambda
in the following way
objective = @(X) sum_square( X(omega) - b )/2;
cvx_begin
variable Xcvx(N,N)
minimize objective(Xcvx)
subject to
Xcvx == semidefinite(N)
trace(Xcvx) <= lambda
cvx_end
In the upper problem you have a matrix multiplication A*X that you want to be as close as possible to b.
But in the lower problem you are setting that X in some indices (omega) has to be as close as possible to b.
I do not get it.
Thanks