Optimization Problem With 5 Variables.

Hello I need help with a problem I have to do.

I have to minimize and find the minimal value of

F =  (x - 3)^2 + (y - 1)^4 + (u - z)^2 + (u - (2 * w))^2 + (u-6)^2 + 12;

Right now the code i have is

function [Fx] = five_var(f,v)
x = v(1);
y = v(2);
u = v(3);
w = v(4);
z = v(5);
Fx = fminsearch(f, v);

Where I input parameters for v and the function F above for f. However, it is not working and I am not sure why because I am, as far as I can tell, utilizing the same process that the mathworks site recommends. Please help!

Answer 1

[Walter Roberson]

F =  @(u, w, x, y, z) (x - 3).^2 + (y - 1).^4 + (u - z).^2 + (u - (2 * w)).^2 + (u-6).^2 + 12;
f = @(v) F(v(1), v(2), v(3), v(4), v(5));

initial = randn(1,5) * 100;

fx = fminsearch(f, initial);

However, notice that your variables are mostly separate. You can see by inspection that at the minima, x = 3, y = 1, and you can see that none of the terms are negative so the +12 is a constant shift, so you can reduce this to a search over three variables (u - z).^2 + (u - (2 * w)).^2 + (u-6).^2 . Simple inspection then shows that the minima would be at u = 6, z = u, w = u/2 . This gives an overall solution of u = 6, w = 3, x = 3, y = 1, z = 6

[Spottswood]

awesome thanks. I had guessed those as my parameters but could never seem to get it working!