Using the Nelder$-$Mead algorithm solve the following optimization problem with starting points $(x,y)=$Solve the following optimization problem using $(1)$ Newton's method, $(2)$ Quasi$-$Newton method and $(3)$

Conjugate Gradient method, starting at $(x_1,x_2)=(1,1).$ In all the cases use the exact line search to

calculate the step length.

minf$(x)=x_1^2-x_1+x_2^2-x_2-4$

Show the iterations.

$\{(-2,-2),(-2,-4),(-3,-4)\}$

minf$(x,y)=(1-x{)}^2+100(y-x^2{)}^2$

Does the method converge? Is the solution provided by the method optimal or just a stationary point?

Compare your solution using the Matlab function "fminsearch".