How can I write a self scaling function for fmincon ?

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Tim 2018-11-28

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https://ww2.mathworks.cn/matlabcentral/answers/432575-how-can-i-write-a-self-scaling-function-for-fmincon

评论： Matt J 2018-11-30

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Hey,

I use fmincon and I want to maximize this function =

fun = @(x) -(x(1)*x(2)*x(3))

and now I do not want to change this function everytime I in- or decrease the size of my optimization.

For example:

If I am looking for 6 solutions my function should look like this =

fun = @(x) -(x(1)*x(2)*x(3)*x(4)*x(5)*x(6))

Is there a way to do it automatically ?

Thank you so much!

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Matt J 2018-11-28

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编辑：Matt J 2018-11-28

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fun = @(x) -sum(log(x))

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Matt J 2018-11-29

编辑：Matt J 2018-11-29

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That's a legitimate concern, but I think it works out because the interior point algorithm is used. The singularities on the boundary can only be approached asymptotically. The bigger problem is that the optimization is ill-posed. Both formulations give me lots of different solutions when I randomize the initial guess,

x0 = 0.5+rand(1,Anz_Var);

In any case, the non-log version is problematic for some reason. It always takes many more iterations to converge, often terminating because MaxIter is reached, and always gets stuck in a local minimum. Here is an amplification of my test code, in which I supply analytical gradients:

x0 = ones(1,Anz_Var);
opts=optimoptions(@fmincon,'SpecifyObjectiveGradient',true,'MaxIter',1e4,'MaxFunEvals',3e4);
[x1, ~,ef1,out1] = fmincon(@fun1,x0,[],[],Aeq,beq,lb,ub,[],opts); fval1=fun1(x1);
[x2, ~,ef2,out2] = fmincon(@fun2,x0,[],[],Aeq,beq,lb,ub,[],opts); fval2=fun1(x2);
fval1,
fval2
function [f,g]=fun1(x)
  f=prod(x(1:6))  ;
  g(1:18)=0;
  g(1:6)=f./x(1:6);
end
function [f,g]=fun2(x)
  f=sum(log( x(1:6)  ))  ;
  g(1:18)=0;
  g(1:6)=1./x(1:6);
end

Tim 2018-11-30

Ah okay. I will try this as well. One additional question came to my mind: Is my code a good way to minimize each of the objective values individually or would you suggest something else?