Use of Fmincon for stress relax data

I have to use "fmincon" to solve the optimization problem for the fitting of an "Stress Relaxation" curve. My aim is to define the coefficient of the Prony Series (gamma_i & tau_i).

The problem is that i don't know how to define my function and start the fitting in order to find e1,e2,e3 & tau1,tau2,tau3.

In Input i have the experimental data (stress relax) and time

fun= E0 * (1 - ( (e1*(1-exp(-t/tau1))) + (e2*(1-exp(-t/tau2))) + (e3*(1-exp(-t/tau3)))))

[Mathieu NOE]

look in the documentation, on this forum and / or internet and you will find plenty of examples , like :

I want to fit my ode model to experimental data and derive parameters using lsqcurevfit and fmincon - MATLAB Answers - MATLAB Central (mathworks.com)

simultaneous curve fitting using "fmincon" - MATLAB Answers - MATLAB Central (mathworks.com)

constraints - matlab: constrained fit with lsqcurvefit and fmincon - Stack Overflow

constrained fitting using lsqcurvefit / fmincon - MATLAB Answers - MATLAB Central (mathworks.com)

How to use fmincon to fit parameters to observed data? - MATLAB Answers - MATLAB Central (mathworks.com)

Answer 1

[Torsten]

I suggest you read the examples for the different suitable solvers. They will show you exactly how to proceed for your case.

Maybe it's better to use a solver especially designed for parameter fitting than fmincon:

fitnlm, fit, lsqcurvefit from the curve-fitting toolbox or fminspleas from the file exchange.