Camel Back $-3$ Three Hump Problem $($CB$3)($Dixon and Szeg$,1975)mi{n}_{x}f(x)=2x_1^2-1\mathrm{.}05x_1^4+\frac{1}{6}{x}_1^6+x_1{x}_2+x_2^2$

subject to $-5x_1,x_{2}5.$ The function has three local minima, one of them is global located at $x^{*}=(0,0)$ with $f(x^{*})=0.$

Write a MATLAB program to find the minimum of the function by $.$using

Newton$-$Raphson,

Hestenes$-$Stiefel,

Polak$-$Ribi$$re and

Fletcher$-$Reeves algorithms. If the function is not differentiable, use an approximation proposed by yourself or an relevant approximation commonly used in the literature and write it explicitly in your report. Repeat the main steps of your algorithms until the desired accuracy is achieved, i$.$e$.$

$||gradf(x_k)||$ and $|f(x_{k+1})-f(x_k)|$