Frobenius Norm and Trace Minimization

Nonconvex
1

Hi All

Can anybody help me to formulate this minimization using CVX. I want to minimize the following quantity where all elements of X are positive and X is an mxn matrix where m is less than n:

norm(X’*X-I,‘fro’)^2

I have tried to reformulate this with Trace equivalent and quad-form and pow_p but I am getting the error below.

Disciplined convex programming error:
Invalid quadratic form: must be a scalar.

I would appreciate it if anybody can help me to solve this using CVX or approximate this and solve it.

Thanks
Mehdi

2

If I’m not mistaken, this is not a convex problem in X. If this is the case, then CVX will not be able to solve it.

3

You are correct.