Question $2$:

Use Gradient Search $($the method of steepest ascent$)$ to approximate the optimal solution to the following problem:

maxf$(x)=ax+x^{T}Qx$

where

$a=[2,1,4]$

$Q=\left[\begin{array}{ccccccc}-3& -2& -1& -4& 0& 0& -1\end{array}\right]$

$-2$

$-2$

$-1$

Begin at the point $x^0=0.$

Apply the algorithm until the length of the gradient vector at a point is less than $1,$ or stop at the fifth iteration.