introduce SECULAR ANTIDERIVATIVE
\[
g_{\mu}(\lambda) = \lambda -
\sum_{i=1}^{n-1}\left(\frac{\hat{\eta}_i^2}{\gamma_i-
\lambda}\right),
\]
\[
g_{\mu}'(\lambda)=f_{\mu}(\lambda)
\]

connections between trust region
problems and perturbation theory

LEMMA
Assume easy case
and let $\lambda \in \Lambda$.  Then
the secular antiderivative's values on the Lagrange multiplier set
$\Lambda$ are precisely the values of the quadratic function $\mu$ on
the corresponding set of stationary points.
\[
g_{\mu}(\lambda)=\mu(x^{\lambda}),
\]
where $x^{\lambda}=(B-\lambda I)^{-1}\eta$.