%   file is   slide15.tex
Standard trust region subproblem

{\bf COROLLARY}
$C=I$, $\beta < 0 < \alpha$
\[
\bar{g}(\lambda) = \lambda \alpha - \psi^t (B-\lambda C )^{\dagger}
\psi.
\]
Then
\[
\mu^* = \sup_{B-\lambda C > 0,~\lambda \leq 0} \bar{g}(\lambda).
\]
In addition, in the hard case,
\[
\mu^* = \sup_{B-\lambda C > 0,~\lambda \leq 0} \bar{g}(\lambda)
     = \max_{B-\lambda C \geq 0,~\lambda \leq 0} \bar{g}(\lambda).
\]