Use MATLAB to solve the following problem

The following function is known as the Himmelblau's function:

$f(z_1,z_2)=(z_1^2+z_2-11{)}^2+(z_1+z_2^2-7{)}^2$

a$)$ Use fminunc to minimize the function with the following starting points and report the

optimized objective function value:

i$.,z^{(0)}={\left[\begin{array}{cc}0\mathrm{.}5& 1\end{array}\right]}^T$

ii$.,z^{(0)}=[4-5{]}^T$

iii. $,z^{(0)}={\left[\begin{array}{cc}-1& 0\end{array}\right]}^T$

iv$.,z^{(0)}=[-3-0\mathrm{.}5{]}^T$

Create two figure, such that figure $1$ shows a surface plot of the function and figure $2$ shows the

contour plot of the function. Use the figures to explain the results obtained in parts $($i$)-($iv$).$

Note: Use the following options to run fminume:

options $=$ optimoptions$(\text{'}$fminunc$\text{'},$'Algorithm', 'quasi$-$newton','Display', 'off'$)$;

b$)$ Use the fminuncBFGs from Problem $4$ to solve parts $($i$)-($iv$)$ from part $($a$).$ Comment on the

difference between the results obtained with fminuncBFGS and fminunc.

Use MATLAB