Bordered hessian

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The complete Hessian of the Lagrangian:

LaTeX: 
\left[ \begin{array}{cc}
H_x[L(x,u,v)] & G^T \\
G &  0
\end{array} \right],
where
LaTeX: 
G = \left[ \begin{array}{cc}
\nabla g(x) & 0 \\ 0 & \nabla h(x)
\end{array} \right].
Here we let LaTeX: H_x[L(x,u,v)] be the Hessian of the Lagrangian (L) with respect to LaTeX: x only. The southwest and northeast blocks are the constraint gradients because they give the cross derivative between LaTeX: x and the Lagrange multipliers LaTeX: (u,v).


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