how to use fmincon in a loop

I have 5 unknown parameters but only 4 equations, but each parameter has an interval, so I prefer to use fmincon. For example, these are 4 equations:

2*x(3) + x(5) + 5*x(1) - 1=0;
x7*(4) + 3*x(3) + x(2) - 10=0;
x(3) + 2*x(5) + 5*x(1) - 3=0; 
3*x(4) + 9*x(5) + x(2) - 10=0;

My idea is like this:

for x(1)=0.1:0.1:1
fmincon(@myfun, x0,[]...)
end

But I do not know how to let x(1) be changed in the loop.

Thank you for any suggestions in advance.

[Amit]

what are the conditions? I think you can solve this without using fmincon

[Cong]

There are no special conditions, but x(1)...x(5) should be less than 1 but larger than 0. And I think I can add this requirement in the fmincon function.

[Amit]

3*x(4) + 9*x(6) + x(2) - 10=0;

is this correct? x(6)? I thought you had only 5 parameters?

[Cong]

Sorry, I just correct my mistake. You are right, only 5 parameters. This is just an example.

Answer 1

[Amit]

A = [5 0 2 0 1;
   0 1 3 7 0;
   5 0 1 0 2;
   0 1 0 3 9];
b = [-1;-10;-3;-10];
FF = @(x) norm(A*x+b);
xx = fmincon(FF,rand(5,1),[],[],[],[],zeros(5,1),ones(5,1))

[Cong]

Hi Amit,

I think you missed my biggest question that I asked: how can I put [fmincon] in a loop. Since there are 5 parameters but 4 equations, so I try to fix a parameter first and then use [fmincon] to calculate others, and then do it in a loop.

[Cong]

Can I put those equations in my script with {fmincon}, instead of writing a function to include my equations?

[Amit]

Cong, Yes, you can definitely put this in a script. However, I don't think this will give you a solution. I have tested the equations you have given here by varying x(5) between 0 and 1 and allowing the rest to be solved as A\b but I could not find an solution satisfying 0< x(i) < 1.

The method I posted earlier, minimizes the function to the minimum value possible but it wont solve it. Are you sure there is a solution for this problem within the ranges you specified?

[Cong]

Hi Amit, the equations that I posted are not my real problem which are more complex and non-linear. Here I just want to get an idea how to vary my x(5) while using 'fmincon'. I figure out that it is a problem of using anonymous function. Here is a simple example, but note that some contents are not provided.

for p=1:10  
    i=i+1;
x(i,:) = fmincon(@(X) myfun(X,p), x0, [], [], [], [], ...
    [], [], [],  options);
end

Thank you for the time.

[Amit]

what is i there?

In a way, lets say you're trying to vary x(5) only, you can do it two way.

1. set the upper and lower bounds for x(5) as value-eps and value + eps, this will contain the value of x(5) within the range.
2. For you objective function, use only 4 input variable and pass the value of x(5) as a scalar as in fmincon(@(x) myfun(x,x5val). In this scenario, you'll have to write the function accordingly.