How can I define a a column of 180 rows as variable "x" in order to use the fmincon function?

Dear all,

First of all, I'd like to say that I'm not experienced in working with Matlab, and please excuse me if I make mistakes.

I have to maximize an objective function using fmincon, as my obj. fun. is a linear programming problem with linear constraints "Aeq" and a non-linear constraint "nonlcon". Basically, my objective function is a sumproduct function : f=sum(a(1:180).*x(1:180)), where a(1:180) are my parameters (known). What I don't know how to do, is to define the X (my 1 column and 180 rows matrix containing 180 variables). Kindly think of X as X(1), X(2) to X(180).

Thank you a lot in advance!

Kind regards, Alex

Answer 1

[John D'Errico]

I suppose if you have nonlinear constraints, fmincon is the solution.

As for how to have that as a function, trivial.

f = @(x) sum(a.*x);

Or, with one less character...

f = @(x) dot(a,x);

Or with even fewer characters...

f = @(x) a'*x;

[Alex Stef]

Dear John,

Thank you for your reply!

After setting the obj.fun. as sum(a.*x); and run the fmincon I've received an error saying "Input argument "x" is undefined"

This is how I defined the obj fun:

          function f = myfun(x)
            a=[[0.684487949143737;1.18483594161165;0.695412371288530;.....-0.106350487000000;]];
            size(a);
            myfun(x)=sum(a.*x);

Am I not supposed to define X, so that it knows I want 180 variables? What do you think?

Thank you so much!

[John D'Errico]

I think you don't know how to write a function so that it returns an argument.

As it is, I showed you how to write that function in a way that did not even need an m-file at all. Anyway, I think you need to start reading basic tutorials. For example, the line

size(a);

in your code does nothing at all. It has no purpose.

If you INSIST on the use of an m-file, do it like this:

function f = myfun(x)
a =[0.684487949143737;1.18483594161165;0.695412371288530;-0.106350487];
f = sum(a.*x);

You need to see and understand the difference.

[Alex Stef]

Dear John, You are correct. I've followed your instructions and eventually I've found some results.

Thank you!

Answer 2

[Walter Roberson]

fmincon passes in x as a column vector to the function. If you define "a" as being a row vector then you can get rid of the explicit sum by using matrix multiplication,

f = a' * x;

where a has been created as a column vector.

It is better to create your "a" outside the function and to parameterize your objective function. Before the fmincon call,

a = [0.684487949143737;1.18483594161165;0.695412371288530;.....-0.106350487000000;];

Then the call itself would be

fmincon(@(x) a' * x, ....)

[Alex Stef]

Dear Walter,

Thank you for the answer. It was really helpful.