How to minimize a function when variables do not appear directly?

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Pasquale 2017-11-3

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评论： Pasquale 2017-11-4

The code is too complicated, so I resume its structure in equivalent way: I choose a start vector x, for example x=[x1 x2 x3 x4] (for my problem it could have more than 1000 elements), and through separate functions I calculate the vectors a,b,c,d. Each of them depends on the previous one, more or less in this way:

 a=f(x);
 b=f(a,par1,par2,par3);
 c=f(b,x,par1,par2,par3);
 d=f(c,par1,par2,par3);

The object function (OF) I want to minimize is very simple, something like OF=d1+d2+d3+d4, but how can I find the vector x that minimizes OF if it does not appear in the function?

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Pasquale 2017-11-3

So if the variable x does not appear directly in OF, it is impossible to use fminnunc or similar minimization functions?

Stephen23 2017-11-4

You just need to pass the parameters to the function exactly as Walter Roberson and the MATLAB documentation show:

https://www.mathworks.com/help/optim/ug/passing-extra-parameters.html

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采纳的回答

Walter Roberson 2017-11-3

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在 MATLAB Online 中打开

par1 = ...
par2 = ...
par3 = ...
func = @(x) minimize_this(x, par1, par2, par3)
[best_x, fval, exitflag, output] = gamultiobj(func, number_of_variables);
function cost = minimize_this(x, par1, par2, par3);
  a=f(x);
  b=f(a,par1,par2,par3);
  c=f(b,x,par1,par2,par3);
  d=f(c,par1,par2,par3);
  OF = a + b + c + d;
  cost = OF;
end

"So if the variable x does not appear directly in OF, it is impossible to use fminnunc or similar minimization functions?"

Not appearing directly in OF is not the problem. You cannot use fminunc or similar minimization functions because your OF is a vector and it is meaningless to minimize a vector.

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Pasquale 2017-11-4

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Thanks for advice, but the problem is a bit different. I need a,b and c only to evaluate d. To make the problem realistic, a is a displacement vector, b are strains, c stresses, and d stress combination, so they can be calculated only one after the other. When I get d, my OF is the sum of the elements of d vector, so it is scalar. For example OF=d1+d2, or OF=d1+d2+d3+d4+d5...+d1000 (vectors x and d have the same length, this depends on the mesh size).

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Stephen23 2017-11-4

编辑：Stephen23 2017-11-4

在 MATLAB Online 中打开

temp1.m

"how can I find the vector x that minimizes OF if it does not appear in the function?"

This does not make sense: x must appear in the cost function for the minimization to make any sense. The problem is that you seem to think that it is required to evaluate all of those functions for some x value before calling fminunc, but this totally defeats the purpose of functions: they can be passed around without being evaluated with specific values.

Instead of this:

x=1;
A=funz1(x);
B=funz2(x);
C=funz3(x);
D=funz4(A,B,C);

you need to stop thinking that you have to evaluate those functions for some x value before using them in your cost function. All you need is to call those functions inside of your main cost function (of course adding the parameters as Walter Roberson showed):

function OF = cost(x)
A=funz1(x);
B=funz2(x);
C=funz3(x);
D=funz4(A,B,C);
OF=2*D-D;
end

"How should I write the function cost, and how write it in the main code?"

Walter Roberson has already shown you exactly how you should solve this task. Thrice. And now me too. What part of this does not work for you? What are you expecting that this solution does not give you?

I even put all of this into one Mfile and attached it to this comment. It runs. It gives exactly the same output as your "simple example" above.

Add the parameters exactly like Walter Roberson showed you already.