Hi,
I want to solve the following optimization problem. (I attached the screenshot of the problem as well in case it is hard to read from latex format.)
$$P=\min \log \det (P^{-1})$$
\[\text{s.t. }
\begin{bmatrix}
A^TP+PA & PB \\
B^TP & -c \\
\end{bmatrix}
\leq 0\] where $P \in R^{n,n}$ and $A \in R^{n,n}$, $B\in R^{n}$, $c\in R$ are known.
The hard constraint can be written as an LMI in in $P_{i,j}$. Semidefine program (SDP) also have LMI constraint but with linear objective in $P_{i,j}$. So, this problem can be considered as a generalization of SDP.
I want to solve this problem using Python or Matlab. I have checked documentation of CVXOPT, CVXPY, scipy.optimize, but could not find a solver specifically for this. I am sure there should be a solver for this problem as it is a well known problem especially in control community. Can anyone point me a solver for this?
Thanks.
You could try PICOS. It implements the determinant maximization of Vandenberghe et al., 1998. See the documentation.
http://picos.zib.de/optdes.html#former-maxdet-formulation-of-the-d-optimal-design-sdp
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