fminsearch with vector function and vector output

Hello, Sorry I think the question is trivial but I can't find any answers on the previous posts.

I have a function ' f ' that depends on a vector ' a ' :

 a = 1:1000;
 f = @(x) (x-a).^2;

and I want to get the minimum of this function for each value of ' a '. Ideally I thought a simple code like

x = fminsearch(f,1);

would generate a vector 'x' of solutions : x = [1 2 3 4 ...]. But fminsearch only works with scalars.

Any idea how to solve this? Thanks

Answer 1

[Walter Roberson]

x = arrayfun( @(v) fminsearch(@(x) (x-v).^2, 1), a );

Answer 2

[Bjorn Gustavsson]

For that function it is rather trivial, so you wouldn't need numerical methods.

For a more general function f(x,a) it might become significantly more problematic. The basic principle of the fminsearch function - cunningly walking around in the variable-space for x looking for lower values of your scalar function requires that the function returns scalar values.

In your case you'd have to do the numerical optimization in sequence for each value of a.

HTH

[Chang seok Ma]

Hello, I know this is a post five years ago, but I have one question about your answer.

I have seen couple of posts that vectorized fminsearch is not recommended but I don't still get why is it.

For example, if I want to solve the following

Y = x^2 + 2*x + 1
Y = x^2 + 4*x + 4
Y = x^2 + 6*x + 9
Y = x^2 + 8*x + 16
...
Y = x^2 + 200*x + 10000

and I want to get (-1, -2, -3, -4, ...,-100) as return.

I think it would be a problem if I want to solve something like

Y = f(x1,x2,x3,...,x30) (multiple choice variables) with vectorized fminsearch.

However, in the example code that I wrote, I thought I am just solving 100 different equations at the same time so using vector as an input for fminsearch shouldn't be a problem because this is just repeating scalarized fminsearch 100 times...

Am I understanding something wrong?