How to define handle for fmincon?

I am doing a minimization for a function using fmincon.

please see attached function code and solver script.

The objective function is defined as f in line 200.

The constraints matrix also ready [Aeq] in line 203.

The equality vector [beq] is in line 207.

The main function script is working very well.

The problem is that I cannot run the solver. (The solver refers to function code terms as "Undefined function or variable"). As if the solver can't find the function although the function and the solver are in the same path.

When I tried to fix that I got error "FMINCON only accepts inputs of data type double.".

Musab

Answer 1

[Matt J]

The main function script is working very well.

Nope. Your cwt.m function is not returning any actual numbers.

    >> out=cwt(x0); class(out)

    ans =

        'sym'

You need to provide actual numeric values for the variables ('delta_a', 'delta_c', 'delta_t', 'Di'). You cannot define them with sym().

Also, Aeq and beq should not be generated inside cwt(). Your cwt_solver() function cannot see them there.

[Matt J]

Musaab Al-Lami's comment moved here:

First of all thank you for your response, and please bear with me because I'm not so good at this.

1- I cannot give exact number to ('delta_a', 'delta_c', 'delta_t'), they are the variables of range (-5 to +5), and Di is the value I want to minimise (Di the result of f).

Can I fix that by assigning random or expected values to ('delta_a', 'delta_c', 'delta_t')?

2- Aeq and beq are calculated inside cwt(). How can I have them "visible" to cwt_solver() ?

3- Also I appreciate if you can explain the code you wrote.

[Matt J]

1-I cannot give exact number to ('delta_a', 'delta_c', 'delta_t'), ... Can I fix that by assigning random or expected values to ('delta_a', 'delta_c', 'delta_t')?

Only you know what it is that you are trying to minimize. If the delta variables don't have specific values, then how can cwt() return a specific value? And if cwt() doesn't return a specific value, then what does it mean to "minimize" it?

2-Aeq and beq are calculated inside cwt(). How can I have them "visible" to cwt_solver()

Create a function that returns these quantities as output and call this function in cwt_solver.

[Aeq,beq]=GetMyConstraints(...);

[x2,fval]=fmincon (@cwt, x0, [], [], Aeq, beq, lb, ub);

3- Also I appreciate if you can explain the code you wrote.

It's your code! I simply called your function cwt(x0) at the value x0=[1;1;1;1] defined in your code cwt_solver to show that the result it returns is not numeric.

[Yaser]

Thanks Matt

Regarding the need for numeric values fro the variables, I think I am getting your point ( slowly:-) )

Now let's say I want to minimise the function Di and my variables are ('delta_a', 'delta_c', 'delta_t'), I made the below simplistic code just as an example.

Do you think this will fix the problem , and give me the numeric values needed for the minimisation in fmincon:

% calculating numeric values for the function Di 

% delta variables are from -5 to +5

for i=1:11;

    delta_a = i-6;

    for j = 1:11
      delta_c = j-6;
      for k = 1:11
        delta_t = k-6;
        x2=[delta_a+delta_c; delta_a; delta_a; delta_a+delta_t];
        Di = (4*x2) + 12
      end
    end
  end

[Walter Roberson]

You overwrite all of Di each iteration of the for loop. There is no point calculating anything except what is needed for the final Di.

[Matt J]

Your example does result in a numeric value for the objective Di (not sym anymore), and so in that sense it is closer to something that FMINCON can process. However, in addition to what Walter said, the Di returned is not scalar. FMINCON expects your objective function code to return a scalar value. It is not clear what it even means to minimize a vector-valued function.

I still don't get the sense that you yourself really know what you want minimized. Here is an example of the kind of function that fmincon expects.

fun=@(x) x(1)^2 + x(2)^2

This function takes a length-2 vector of numbers as input and returns a single number as output (in double floating point form),

    >> out=fun([1,2]), numericType=class(out)

    out =

         5

    numericType =

        'double'

Because the output is a number, it can be compared to other numbers, e.g.,

    >> fun([1,2])>1

ans =

    logical

     1

and therefore fmincon can search for its minimum value, e.g.,

    >> [optimalX,optimalVal]=fmincon(fun,[1,2],[],[],[],[],[0;0])

    optimalX =

       1.0e-03 *

        0.7017    0.7024

    optimalVal =

       9.8582e-07

[Yaser]

Thanks Matt for your support and patience

What I want to minimise is the " f " at line 200. It is my objective function.( and f is the same Di )

Now I understood that the value must be scalar not vector, which it is in the code.

But I still cannot take the variables ('delta_a', 'delta_c', 'delta_t') out from the objective function of " f ".

You are telling they should be numerical values.

These are the variables I need the fmincon to find their value.

I don't have a value for them. They are like x(1) and x(2) in your example.

Maybe I have a fundamental misunderstanding about fmincon. I think it is not I who should provide the numerical values for x(1) and x(2). Am I correct?

I think that I should put a function in terms of variables not numbers, say (fun = X(2) + 3(x)^2) and fmincon calculates the numerical values of x(1) and X(2) that gives the minimum value of fun.

I hope I'm right.

and thank you again

[Yaser]

Thank you Walter

Anyway I'm still at a very low level in MATLAB skills

[Matt J]

These are the variables I need the fmincon to find their value. I don't have a value for them. They are like x(1) and x(2) in your example.

If the delta_ variables are the unknowns you are trying to solve for, then they need to form the input vector to the objective function routine cwt(). In other words, cwt.m should have the general structure below. FMINCON will pass various test values for the vector "unknowns" to cwt() until it finds a minimum.

function f = cwt(unknowns)

      delta_a=unknowns(1);
      delta_c=unknowns(2);
      delta_t=unknowns(3);

       ...

    f= ... computations with delta_a,delta_c,delta_t ....

end

Note that in your original code, you do not have this. The input x2 designated in the first line,

   function f = cwt(x2)

is never used in the calculation of f, because it gets overwritten in line 185 where you have,

x2 = [delta_a+delta_c; delta_a; delta_a; delta_a+delta_t];

It also appears from line 185 that x2 is not even the thing you are trying to solve for. It is itself some intermediate quantity depending on the unknowns delta_a,c,t. So, x2 should not form the input to cwt().

[Yaser]

This did solve it.

Thank you so much