Given two 2x2 matrices and the following problem without restrictions, which value of $\alpha$ minimizes the spectral radius (the absolute value of the maximum eigenvalue), of both matrices ($\alpha$ must be the same).
$f(x) = \frac{1}{2}*A^{t}*Qx$
$Q = \begin{bmatrix}1&\\&b\end{bmatrix} $
b between (0,1)
\begin{bmatrix}1&-\alpha\\1&-\alpha\end{bmatrix} \begin{bmatrix}1&-\alpha\\b&-\alpha *b\end{bmatrix}