Struggling with fminsearch with vector inputs

Hello,

I am trying to use vector as an input for fminsearch.

clear
clc

R         = 1.0080;
sig       = 0.75;

tempkgrid = linspace(-20,60,10)';
kgrid = [tempkgrid ; tempkgrid ; tempkgrid];

zgrid = [2;2;2;2;2;2;2;2;2;2;4;4;4;4;4;4;4;4;4;4;6;6;6;6;6;6;6;6;6;6];

K           = kgrid;
Z           = zgrid;

aconst1      = -20*ones(30,1);
aconst2      = 60*ones(30,1);

obj         = @(Kp) (1/(1-1/sig)) * ((Z + K - Kp./R) > 0) .* (Z + K - Kp./R).^(1-1/sig) + ((Z + K - Kp./R) <= 0) * (-999999);

Kp2           = fminsearch(obj,aconst1);

If I run this, I get the following error message. 'Unable to perform assignment because the size of the left side is 1-by-1 and the size of the right side is 30-by-1'

Is there anyway I can run this?

Thanks in advance.

Answer 1

[Matt J]

Your objective function is not returning a scalar value at Kp=aconst1. We cannot know what objective you truly intended.

Regardless though, you will not have much luck using fminsearch on a problem with 30 unknowns. It is designed for much smaller problems (<7 unknowns or thereabouts).

[Chang seok Ma]

Hello, thanks for the answer.

So I intended to return a vector(Kp) that minimizes the objective function and starting point as aconst1.

I changed the code to scalarize the objective function.

Kp3        = fminsearch(@(c) norm(obj(c)) ,aconst1)

and I think it returns the value as I intended.

Could you give me more details about 'It is designed for much smaller problems'?

Does it mean that fminsearch is not suitable for vector?

[Matt J]

It is theoretically proven to converge only for problems with a single unknown, but empirically, it tends to work well up to about 6 unknowns.

https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method

Also, the computation time per iteration can increase steeply with the number of unknowns, N. The algroithm requires N+1 evaluations of the objective function per iteration, so if each evaluation is O(N), the computational cost of the whole iteration will be O(N^2).

Answer 2

[John D'Errico]

Fminsearch should NEVER be used with more than around say 6-8 unknowns. 30 unknowns is just impossible for fminsearch. PERIOD. I've not even looked at whether your problem is well-posed, as fminsearch is a waste of your time here.

[Chang seok Ma]

Thanks for the comments.

I am sorry but I am getting confused.

I intended to solve 30 equations with 30 unknown. However, each equation is independent. So it is just 30 different univariate functions.

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

Y = f(x1,x2,x3,...,x30)

but here is what I intended with different samples

Y = x^2 + 2*x + 1

Y = x^2 + 4*x + 4

Y = x^2 + 6*x + 9

Y = x^2 + 8*x + 16

.....

I just wanted to get (-1, -2, -3, -4, ...) as return.

Does this still cause a problem in fminsearch?

Thank you.

[Matt J]

You can always try, but I think it will be both more reliable and faster if you solve one equation at a time using fzero(). Or, if your eqautions happen to be polynomials like above, you should use roots().