Trace and non-smooth constraints using CVXOPT

[Agniva Chowdhury]

Hi guys,

Is it possible for CVXOPT to solve the following SDP?

Z is the variable

maximize Trace(A * Z)

subject to: Trace(Z) <= 1,  1^T *|Z|* 1 <= k    

Here A, Y  are symmetric PSD, 1 is the vector of all ones, and |Z| is the matrix of the absolute values of Z .

Thanks

Agniva

[Martin]

Yes, this is an SDP and you can solve it with CVXOPT. If you're unsure about how to call CVXOPT directly, you may want to use a modeling tool such as CVXPY (https://www.cvxpy.org) to set up your problem. CVXPY can call CVXOPT and a number of other solvers as well.

Martin

[Agniva Chowdhury]

Thank you so much, Dr. Andersen for getting back to me. The problem is that using CVXOPT through CVXPY severely limits the dimension of the matrix to a few thousands. If it goes beyond that, CVXPY flags a memory issue. Do you have an idea how to address this? The dimension of my data matrix A is about 40k x 40k.

Thank s in advance for your help.

Best,

Agniva

[Martin]

Unfortunately, a general-purpose interior-point method such as CVXOPT is not really suited for large problems of this form. Perhaps there is exists a specialized solver?