# Definition of Objective function in fmincon when it's not an analytic function

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Itachi on 3 Sep 2012
Hi guys, I want to be able to define the objective function when it's not an analytic function. In my code I'm doing analysis by FEM to find a value for displacement in each iteration but I don't have the displacement function itself. How can I minimize displacement (Objective function) then?

Alan Weiss on 4 Sep 2012
You have some function that evaluates the objective, right? Maybe an interpolation as in the Mount Washington example. Toolbox functions don't care what the objective function is, they just need to be able to get function evaluations.
If your objective function is not smooth, as often happens when the evaluation is a simulation or numerical solution of an equation, then you might need to set the finite differences to be larger than default. use the FinDiffRelStep or DiffMinChange options. Or use patternsearch if you have Global Optimization toolbox.
Good luck,
Alan Weiss
MATLAB mathematical toolbox documentation

Itachi on 4 Sep 2012
Thanks, in "fmincon" the objective function is an analytic function, I'm saying in my case where I find the values of the "fun" by numerical methods like FEM what should I put instead of "fun" in here:
x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon)
Alan Weiss on 4 Sep 2012
My question to you is, do you have a function that evaluates the objective? Is it a file on your MATLAB path? I suppose the answer is yes, and your function looks something like
function objective = mycalculation(x,a,b)
...
where a and b are parameters, and x is the vector of control variables. Then you should write
fun = @(x)mycalculation(x,a,b);
For more details, see Writing Scalar Objective Functions.
Alan Weiss
MATLAB mathematical toolbox documentation
Itachi on 7 Sep 2012
Thanks.