Minimization problem (FMINCON): I am unable to minimize my function: "Not enough input errors" and others

I have written a function mydifference(a,s) where a and s are two scalars. The function uses also two vectors of data which I have preferred to import on my script and not putting the as inputs in my function. The code is roughly:

function [ sum_err ]=mydifference(a,s)
err=[];
myimport;
sum_err=sum((1/45)*((p'-(exp((((s^2)/2*a^2)*t)- blablabla ... ;

where in myimport I import vectors of data p and t. The function works for a reasonable value of parameters a and s

When I try to minimize this function changing parameters a and s using the fmincon I do not get any useful result. My code for minimize it is:

myimport;
x=[];
X0=[0.085,0.0015];  %starting values
lb=[0.0001,0.00001];  % "a" not lower than 0.0001 and "s" 0.00001 
ub=[10,5];% "a" not higher than ..ecc ecc
fun=@(a,s)mydifference(a,s);
[x,fval] = fmincon(fun,X0,[],[],[],[],lb,ub)

The errors I get are:

>> min_mydifference Not enough input arguments.

Error in min_mydifference>@(a,s)mydifference(a,s)

Error in fmincon (line 535) initVals.f = feval(funfcn{3},X,varargin{:});

Error in min_mydifference (line 7) [x,fval] = fmincon(fun,X0,[],[],[],[],lb,ub)

Caused by: Failure in initial objective function evaluation. FMINCON cannot continue.

I have computed the correct set of values by using another script which plots on a surfice the values of mydifference and adeguately choosing a and s I can find the minimum of mydifference. This is a very empirical way of doing it and I need to correctly use fmicon to get the same results.

the vector X0 uses good starting values for mydifference

What I think is that fmicon puts X0 directly in mydifference as a single input and this leads to some problems. What I mean is that fmincon performe mydifference(X0) instead of mydifference(X0(1),X0(2)). Same for my vector lb and ub.

Answer 1

[dbmn]

I think the solution might be in the way you created your function fun.

if you check the documentation for fmincon it states that it accepts only one input

"fun is a function that accepts a vector or array x and returns a real scalar f, the objective function evaluated at x."

so you might be better of, if your function fun only accepts one array x with x(1) = a and x(2) = s

I would suggest you change your function to

mydifference(x)
a = x(1); s = x(2);

and change

fun=@(x)mydifference(x);

and

x0 = [a0, s0];

[enzo fiasco]

Thanks! following your suggestion my minimization code now run smoothly! I was thinking the same but I was not able to put my thoughts in practice; thanks again for your answer.