Problem $0$

Implement the modified LDL Newton method. Modify the LDL code given in the slides

to achieve a pd Hessian.

Now test your code with the function

$f(x_1,x_2)=(w_{31}(w_{11}{x}_1+w_{12}{x}_2+b_1)+w_{32}(w_{21}{x}_1+w_{22}{x}_2+b_2)+b_3),$

where

$(x)=\frac{1}{1+e^{-x}}.$

Choose your own parameter values for $w_{i,j}\text{'}$s and $b_k\text{'}$s$.$