Suppose you have an objective function to minimize:

$242$ f x y x y x $(,)3\mathrm{.}52=++$ x xy y $2$

$1)$ Create a contour plot of the objective function over the domain of $2$x $2$

and

$2$y $2$

and print it out. This can be conveniently done using the following code:

xVec $=$ linspace$(-2,2,101)\text{'}$;

yVec $=$ linspace$(-2,2,101)\text{'}$;

$[$x$,$y$]=$ meshgrid$($xVec$,$yVec$)$;

f $=-3\mathrm{.}5*$x $-2*$y $-$ x$.^2+$ x$.^4-2*$x$.*$y $+$ y$.^2$;

figure$(1)$

clf

contour$($x$,$y$,$f$,42)$

grid

If you are unsure what some of those MATLAB commands do$,$ please consult the

MATLAB documentation file $($i$.$e$.$ type doc into the Command Window and press Enter$)$

or ask your instructor.

$2)$ By hand, perform two steps of a steepest descent algorithm using a step size of $2$ starting

from an initial guess of $(-2,-1).$ By hand, draw the corresponding steps as vectors on the

contour plot from Part $1$ to demonstrate how the algorithm is approaching the minimum.

$3)$ Solve for the unconstrained minimum of the objective function using fminunc. Have

your code print the minimum location to the Command Window as: