% file is s19.tex
\[ Q^c := \left[ \begin{array}{cc}
   0 &  \frac 12 c^t \\
  \frac 12 c &Q    \end{array}  \right].
\]
\[
 q^c_u(y) :=   y^t( Q^c-\diag(u))y+u^te
\]
-----------------------------------------\\
relaxed problem
\[
\begin{array}{c}
  ~~(RP^3_u)~~~~f_3(u) := \max_{||y||^2=n+1} q^c_u(y)\\
   = (n+1) \lambda_{\max} (Q^c - \diag (u) ) + u^te.
\end{array}
\]
bound
\[
  B_3 := \min_{u^te=0} f_3(u) = \min_{u} f_3(u).
\]