% file is  s22.tex 
Lagrangian
\[ L_1(v,\Lambda) :=f_1(v) + \trace \Lambda (Q-\diag(v)), \]
where $\Lambda$ is a symmetric, positive semidefinite Lagrange
multiplier matrix.

Optimality conditions:
\[
\begin{array}{c}
0 \in \partial f_1(v) - \diag(\Lambda)~~~\mbox{ (stationarity)}\\
\trace  \Lambda (Q-\diag(v)) = 0~~~ \mbox{ (complementary~slack)}\\
\Lambda = \Lambda^t \geq 0~~~ \mbox{ (multiplier~sign)}.
\end{array}
\]