Problem with minimizing optimization function with multiple variables

I'd like to minimize the function "x^2 +5y^2 +4xy-30x-60y+219". When I did it by hand, I got my minimum to be at 0,15, but I'd like to double check.

My total program is:

function b = f(v)
x = v(1);
y = v(2);

b =  (x^2 + 5.*y^2 + 4.*x.*y -30.*x - 60.*y + 219);
v = [0,15]; %guess
a = fminsearch(@f,v)

When I ran the program, the program gave me an error that I didn't have enough input arguments. I think I had enough, since similar programs had similar code.

Answer 1

[Walter Roberson]

function a = f_driver
 v = [0,15]; %guess
 a = fminsearch(@f,v);

function b = f(v)
x = v(1);
y = v(2);

b =  (x^2 + 5.*y^2 + 4.*x.*y -30.*x - 60.*y + 219);

Answer 2

[John D'Errico]

Defining this m-file...

function b = myfun(v)
  x = v(1); y = v(2);
  b = (x^2 + 5.*y^2 + 4.*x.*y -30.*x - 60.*y + 219);

Now, test it out.

v0 = [0,15];
vfinal = fminsearch(@myfun,v0)

vfinal =
         15  -2.9839e-05

Is the solution correct? Of course. We can verify that.

syms x y
fsym = (x^2 + 5.*y^2 + 4.*x.*y -30.*x - 60.*y + 219);
sol = solve(gradient(fsym) == 0,x,y)
sol = 
  struct with fields:

      x: [1×1 sym]
      y: [1×1 sym]

sol.x
ans =
15

sol.y
ans =
0

Since you don't show how you tried it out, I cannot know why it gave you that error. My guess is you are still at the novice stage where you think you can use the "run" button on everything. I wish they would just get rid of the run button in the editor.