Hi,

I want to solve the following optimization problem.

$$P=\min \log \det (P^{-1})$$

$$[\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. Can anyone point me a solver for this?

Thanks.