Using log_det with non symmetric matrices

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.

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

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.

Afraid not, no.