%file is s11.tex
Now, from the optimality conditions, there exists an optimal
multiplier $\lambda^*$. Let $\nu^*$ and $\omega^*$ be chosen as in
the statement of the Theorem. Then
\[
\begin{array}{rcl}
  \mu^* & = & L(y^*,\nu^*,\omega^*) \\
     &=&  \phi(\nu^*,\omega^*) \\
      & \leq & \max_{\nu \leq 0,\omega \leq 0} \phi(\nu,\omega),
\end{array}
\]
i.e. this and  the previous equations imply that
the first equality holds.

If the easy case holds, i.e. $y^* = (B-\lambda^* C)^{-1} \psi$, then
\[ h(\nu^*,\omega^*) = L(y^*,\nu^*,\omega^*) = \mu^*.
\]
The conclusion follows.