% file is s5.tex
{\bf THEOREM}
$y$ feasible point and CQ:
\[
Cy = 0~\mbox{implies}~\beta < 0 < \alpha.
\]
Then $y$ \underline{global} minimum\\
\underline{iff}\\
there exists $\lambda \in \Re$ such that
\[
(B-\lambda C)y = \psi \mbox{~(stationarity)},
\]
\[
B-\lambda C \geq 0 \mbox{~(Hessian~nonneg~def)},
\]
and
\[
\lambda (\beta - y^tCy) \geq  0 \geq \lambda( y^tCy-\alpha ) 
~\left( \begin{array}{c} 
    \mbox{compl~slack} \\ 
          \mbox{mult~sign~}  \end{array}
       \right)
\]
~\\
\[ B-\lambda C >0~\mbox{implies unique min}
\]