Using log_det with non symmetric matrices

Nonconvex
1

Hi,

I wish to implement the following cost function in CVX:

maximize log(abs(det(A)))

where abs is the Matlab function and stands for ‘absolute value and complex magnitude’ and A denotes a real, ‘non symmetric’ square matrix of full rank.

I understand that we can implement maximize( log_det(A) ). However, this returns optimal A as symmetric matrix which I wish to avoid.

Any help would be much appreciated.

Thanks.

2

Unfortunately, log_det is concave only for symmetric matrices. What you seek to do is not possible in CVX.

3

Thank you for your reply. Would you happen to know if there is some other optimization software which I can use for such a cost function subject to LMI constraints on A.

4

Afraid not, no.