How to transform the semidefinite program (SDP) $$ \min \, \, c^T x $$ $$ \text{subject to}\,\, F(x)>0 $$ where $F>0$ is a LMI ($F(x)=F_0 +\sum_{i=1}^n x_iF_i(x)$, $F_i$ symmetric matrix) and $c$ is a vector of $R^n$, into the eigenvalue problem (EVP) $$ \min \, \, \lambda $$ $$ \text{subject to}\,\, \lambda Id - A(x) >0 \quad B(x)>0 $$ where A,B are symmetric matrices which depend affinely on x.
This problem comes from page 10 of Linear Matrix Inequalities in System and Control Theory:
