%  file is   s4.tex
General Trust Region Subproblem:
\[
(P)~~~~~~~\begin{array}{cll}
    \mu^* :=\min  ~~ \mu(y) & := & y^tBy-2\psi^ty \\
{\rm subject~to} & \beta \leq &y^tCy  \leq \alpha,~ y \in \Re^n
            \end{array}
\]

$B$, $C$ symmetric, possibly indefinite
\[ -\infty \leq \beta \leq \alpha \leq \infty \]

\begin{itemize}
\item
{\bf characterize} global min
\item
concave max dual problem with no duality gap
\item
( can characterize local min )\\ 
(connections to eigenvalue perturbation problems)
\end{itemize}