Optimization Problem With 5 Variables.
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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!
采纳的回答
Walter Roberson
2016-10-19
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
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