Example $7\mathrm{.}4$

Minimize $f(x_1,x_2,x_3)=(x_1-x_2{)}^2+(x_2-x_3{)}^4$

subject to

$g_1(x)=x_1(1+x_2^2)+x_3^4-3=0$

$-3x_{i}3,i=1,2,3$

Create the Matlab code for the Example given under the topic heading. Algorithms will be created without using Matlab optimization built$-$in functions. The trajectory followed by the algorithms will be drawn on the function in Matlab and the resulting optimization point will be marked on the function.