Equivalent of Excel Solver, fminunc?

I'm replicating a calculation done in Excel with Matlab. The spreadsheet used Solver to find the smallest difference between a given value and an estimated value from a known function. The function is y=a+b*exp(c*x) where parameters a, b and c are to be estimated, x is the age. The formula is applied for range of ages and the minimum is the square difference (y_given-y_estimated)^2.

I'm able to use the function fminunc for one age but struggle to have this to a range of ages. My program looks like this

    param0 = [0,0.2,1.2];
    fun=@(param)f_Makeham(param0,y_given);
    [S2, fval]=fminunc(fun,param0);

    function res = f_Makeham(param,y_given)
    x=(77.5:1:100.5)';
    res = a0+b0.*exp(c0.*x);

This obviously generates an error.

How can I change the program to consider the minimum difference for a range of ages, and estimate a, b and c for those ages?

Answer 1

[Torsten]

function res=f_Makeham(param,y_given)
a0=param(1);
b0=param(2);
c0=param(3);
x=(77.5:1:100.5)';
res=sum((a0+b0*exp(c0*x)-y_given).^2);

[Orongo]

I get fval same as param0, hence no optimization (I also tried for different values on param0).

[Torsten]

S2 are the fitted parameters ...

[Orongo]

Sorry, typo. I mean S2 is matching param0

[Torsten]

Could you include a plot of y_given vs. x ?

[Orongo]