%   file is s7.tex
Existence or boundedness\\
 {\bf equivalent to}\\
 positive semidefinite pencil

{\bf THEOREM (EXISTENCE-BOUNDEDNESS)}
$C$ nonsingular
\begin{itemize}
\item
$(P)$ possesses a minimizing point and\\ $\max\{|\alpha|,|\beta|\}>0$
implies positive semidefinite pencil condition holds.
\item
Conversely, positive
semidefinite pencil condition
and regular implies
minimizing point exists
\end{itemize}