Problems with fminsearch giving startvalues as result

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Marc Laub 2022-4-25

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编辑： Matt J 2022-4-28

Hey,

I am trying to minimize Gibbs enthalpie dependant an phase fraction and phase compositions. So i set up an equation which has all dependencys in it and is dependent on 2 variables.

The problem is that fminsearch is doing nothing, it always gives ma my start values back as results. From the outout I can see that it did 39 iterations ans tells me that the result lie within the TolX and Tolfun, but thats not the case. With a simple parameter sweep I get better results than fminsearch.. I also changes Tolx and Tol fun to very small values but that didnt help either. No matter how stupid my starting values are, thats its result, no matter how bad it is.

I also had this phenomen when doing fits with custom functions, sometimes als here that start values were given back as fit parameters without any improvement.

Does anybody know what I am doing wrong?

Many Thanks in advance.

Best regards.

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John D'Errico 2022-4-25

编辑：John D'Errico 2022-4-25

Very often this happens because people don't understand optimization tools. For example, is your function discrete in some way, quantized? Fminsearch CANNOT solve such a problem, because it assumes the objective is a well-behaved function of the parameters (essentially, smooth.) This will cause it to terminate, despite there being better solutions elswhere, since in the vicinity of your start point, the function is essentially constant.

Similarly, even if the function is indeed well defined and everywhere differentiable, your function might just be so flat that it cannot see a way to move that is any improvement, to within the tolerance. So it gives up, returning your start point.

Another common failure is when people use random numbers in the objective. Doing so makes the function not smooth in any respect. And again, fminsearch will almost certainly fail to converge to a good solution. (It might work for a bit if there is a sufficiently large signal beyond the random component in the function, but it will eventually get hung up.)

All of these cases will cause fminsearch, or indeed, most optimization tools to fail to iterate. Is your problem among the general classes I mentioned? Who knows? You may just have a bug in your code, and are calling the optimization tool incorrectly.

Walter Roberson 2022-4-26

Are you truly working with polynomials? Or are you working with multinomials? Do you have any terms which end up using variable_1 * variable_2, or could it be separated out into the sum of two polynomials each in a single variable?

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采纳的回答

Matt J 2022-4-26

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编辑：Matt J 2022-4-27

在 MATLAB Online 中打开

With a simple parameter sweep I get better results than fminsearch.

I don't know how you've implemented the sweep, but I don't see why you don't use that as your solution, or at least use it to initialize fminsearch. Since you know a local region where the minimum is located, I picture the sweep done in a vectorized fashion like below. It should be easy to vectorize the operation in fun() if they are just polynomial operations.

[var1,var2]=ndgrid(linspace(__), linspace(___))
Fgrid=fun(var1,var2) ; %vectorize fun() to accept array-valued input.
[~,iopt]=min(Fgrid(:));
var1_optimal=var1(iopt);
var2_optimal=var2(iopt);

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Marc Laub 2022-4-27

I got 2 systems which share some constituents. So I have as many variables, relativ content of my systems, as they have constituents. System 1 is composed of like 4 constituants with the relativ composition values d1,d2,d3,d4,d5(=1-d1-d2-d3-d4) and system 2 is composed of only 2 constituents c1 and c2. Since c1=1-c2 I can reduce System 2 on 1 variable. Now the composition of system 1 depends on the composition of system 2, so on c1, and on how much of system 2 I am extraction from system 1, called f, because of the mass balance.

I now have to describe the energy of my systems. Those are described by taking the energy of the constituent weighted pure constituents described by p1(T)=d1*(a+b*T+c*T*log(T)+d*T^2+e*T^3+f*T^(-1)+g*T^(-2)+h*T^(-3)+i*T^(-9)+j*T^(4)); for each constituent. Then more additional excess terms which compensate for missing interaction in the equation above are also weighted and added. They follow the same structure as the equation above, but often with variables c,d,e...,j=0. All those are added up and give me the energy for system one. Same is done for system 2.

To account for mass balance, the value in system 1 for the constituents both systems are sharing, is depended of the composition of system 2 and on how mich system 2 I have...

So Energy of system 1 is kind of

E1=sum(p1_1,p2_1,p3_1,p4_1,p5_1,..) all p dependend on (d1(c1),d2(c1),d3(c1),...d15(c1),f) (index _1 for system 1)

and system 2 is

E2=sum(p1_2,p2_2,p3_2,p4_2,p5_2,..) only dependend on c1

Energy of the whole system is then the weighted some of both systems

E_total=(1-f)*E1+f*E2; and this has to be minimized

Marc Laub 2022-4-28

yeah I end up with log() of the unknows.

Thats also why I have to go with fminsearchbnd, since fminserach finds minimums for negative values, beaucause log() of some negative values gives easy highly negative and therfore probaply minimum values... but negative values of the unknown dont make sence physicaly, therefore the necessity of a bound.

The ...T^(-1) and T^(-3) terms are only dependend on T and therefore constant for each individual case. They are pre calculated and then just insertet. The results of the ...T^(-1) and T^(-3) terms are only weighted by the unknown either just by multiplication with one unknown or more, multiplication with the difference of unknowns or weighted by the difference of unknowns to the power of 2

Matt J 2022-4-28

编辑：Matt J 2022-4-28

Just make the change of variables var1-->var1^2, var2-->var2^2 to ensure they only present positive values to the objective function. That's what fminsearchbnd does anyway.

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