optimal values of input values to a function based on data

I have a function which takes parameters - a,b,c,d,e and the returns the computed value z.

I also have the ground truth values of z. I would like to compute the optimal parameters of a,b,c,d,e which would minimize the error between the ground truth value z and the approximated value of z by the function.

I have data for the computed values of z and the ground truth values z given different input values of a,b,c,d,e.

z1 = function (a1 + b1 + c1 + d1 + e1) and error1 = (z1 - z1') where z1 is returned value and z1' is the ground truth
z2 = function (a2 + b2 + c2 + d2 + e2) and error2 = (z2 - z2') where z1 is returned value and z2' is the ground truth
....             ....               ...                ....          .... .              .... 
zn = function (an + bn + cn + dn + en) and errorn = (zn - zn') where z1 is returned value and zn' is the ground truth

Any suggestions how to find the optimal parameters of a,b,c,d and e using Matlab?

I was thinking of optimization solver to get optimal values of a,b,c,d,e for my data but I am not sure how to proceed.

Thanks a lot for your help in advance

Ash

Answer 1

[Alan Weiss]

This sounds like Curve Fitting via Optimization. If you have Optimization Toolbox™, you can also look for suggestions in Nonlinear Data-Fitting.

Alan Weiss

MATLAB mathematical toolbox documentation