Derive the formula (B.25) for a diagonal Hessian update in a quasi-Newton method for minimization. In other words, given a current minimizer \(\boldsymbol{x}_{t}\) of \(f(\boldsymbol{x})\), a diagonal matrix \(\mathbf{C}\) of approximating the Hessian of \(f\), and a gradient vector \(\boldsymbol{u}=abla f\) \(\left(\boldsymbol{x}_{\boldsymbol{t}}\right)\), find the solution to the constrained optimization program:

\[ \min _{\mathbf{A}} \mathscr{D}\left(\boldsymbol{x}_{t}, \mathbf{C} \mid \boldsymbol{x}_{t}-\mathbf{A} \boldsymbol{u}, \mathbf{A}\right) \]

subject to: \(\mathbf{A g} \geqslant \boldsymbol{\delta}, \mathbf{A}\) is diagonal, where \(\mathscr{D}\) is the Kullback-Leibler distance defined in (B.22) (see Exercise 4).