# Can I use fmincon with a whole model as function?

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Timo Beune on 21 Jun 2024
Commented: Timo Beune on 24 Jun 2024
I am currently working on an optimization for a flow and electric current problem. The parameters to be optimized are geometric parameters like lengths, diameters, thicknesses of channels etc. I want to use fmincon, but to my understanding I would need to define a function that is dependent on my variables. However the problem itself needs to iterate before a solution is found. Therefore, fmincon would need to put the values of x into the flow and current model, calculate values for current efficiency and pressure drop, and then use these values to optimize. Is that in someway possible? and if yes, how would I define fmincon and the function itself? The model itself is too big to put in, but i will try to give an example:
The value of Dp depends on the input parameters defined in x and the same goes for Ic,k but cannot immediatly be linked to them since they first need to iterate. Fmincon then needs to find an optimum for the system efficiency, which is defined as . So basically my function would be something like , where x is a vector containing values for channel length, diameter, depth etc. Hopefully this is somewhat clear.
Sam Chak on 21 Jun 2024
Hi @Timo Beune, the MATLAB code for writing the objection function has been provided by @Torsten.
Because fmincon() only minimizes the objection function, if you wish to maximize the system efficiency, then the objection function should be written as
,
unless I misunderstand the concept of optimality in system efficiency.
Torsten on 21 Jun 2024
Thanks for the minus - I added it below.

Torsten on 21 Jun 2024
Edited: Torsten on 21 Jun 2024
You call "fmincon" as
sol = fmincon(@fun,x0)
and write a function "fun" as
function obj = fun(x)
% Compute P_p from x (maybe by iteration or even software different from MATLAB)
% Compute eta_i from x (maybe by iteration or even software different from MATLAB)
obj = -eta_i/P_p
end
Timo Beune on 24 Jun 2024
Thanks. It was namely a matter of code construction, not so much a problem. Thanks for your help