Minimize non linear function with undefined vector

I have to do the picture's question.

I already built a function for the function to minimize:

function z=f(x)

n = size(x,2);
z = symsum(100(x(1,i)-x(1,i-1).^2).^2 + ...
(1-x(1,i-1))^2,i, 2, n);
end

Now, I want to use the fminunc matlab function to finish the exercise. However, I have several questions:

1) I don't know where I can mention that x is the 2d vector, then 10, 100, 1000? 2) As there is no specifications about x0, I don't know how to say that I want to start from - infinite.

Any ideas?

Answer 1

[Torsten]

The examples given here should show you how to proceed:

https://de.mathworks.com/help/matlab/ref/fminsearch.html

[Nolwen Brosson]

In this link, it's only a 2d vector, si you can simply write by hand the function. Here, I want to generalize it for different values of n.

[Torsten]

function main
  n = 10000;
  x0 = zeros(n,1)
  sol = fminunc(@fun,x0)
end

function z = fun(x)
  z = 0;
  for i = 2:numel(x)
    z = z + ...
  end
end

Can you fill the "..." with your function definition ?

[Nolwen Brosson]

Thank you for your code. So, if you say that x0 is a n-dimension vector, matlab know that x (in the fun function), will be a n-dimension vector?

I still have an error, but I guess the hardest part is done :)

n = 10000;
x0 = zeros(n,1);
[sol, fminval] = fminunc(@fun,x0);

function z=f(x)

z = symsum(100*(x(1,i)-x(1,i-1).^2).^2 + ...
(1-x(1,i-1))^2,i, 2, numel(x));
end

[Torsten]

Numerical solvers don't work with symbolic variables. Just fill the '...' with the expression you want to sum.

[Nolwen Brosson]

function main
  n = 10000;
  x0 = zeros(n,1);
  [sol, fminval] = fminunc(@fun,x0);
end

function z = fun(x)
  z = 0;
  for i = 2:numel(x)
    z = z + 100*(x(i,1)-x(i-1,1).^2).^2 + ...
    (1-x(i-1,1))^2
  end
end

[Nolwen Brosson]

I get this error with this code: fminunc stopped because the size of the current step is less than the default value of the step size tolerance.

[Torsten]

For which value of n did you get this message ?

Start with small values for n.

And you should remove the semicolon behind

[sol, fminval] = fminunc(@fun,x0);

to see the solution.

[Nolwen Brosson]

Oh yeah it works !!! Thank you !! It was just the semicolon. Thanks !!

Answer 2

[Bruno Luong]

I'll save you some headache: the solutions are clearly

x = ones(n,1);

[Nolwen Brosson]

I know, but I just want to solve it with matlab