How can I solve this?

Hello everybody!

I critically need to solve the following problem. Could you please let me know, how can I solve the following optimization problem in CVX/MATLAB?

X_opt = min_{X} f(X) s.t. (X^T H X – R) \in {PSD or NSD}

•X is a matrix in R^(m x n) (n >= m)
•f(X) = (Y – X C )^T(Y – X C), where Y \in R^m and C\in R^n.
•PSD(NSD) denotes positive (negative) semi-definite.
•R and H are real symmetric PSD matrices (R^T = R >=0), (H^T = H >=0).
Actually, I don’t know, how I can represent the constraint properly.

Thank you for your time.

Regards, Farhad

5 1.2 years in arrears, but anyhow …

Solve two separate problems, with respectively
X'*H*X - R == semidefinite(m)
-(X'*H*X - R) == semidefinite(m)
and pick the lower optimal objective of the two.