# What is model free Numerical Optimization method?

Numerical optimization method is the model free method using non-linear least square optimization. It is created by Kinetics Neo Team in NETZSCH and implemented only in Kinetics Neo software.

Numerical method searches optimal functions **Ea(alpha)** and **logA(alpha)** in order to get best fit for the **conversion (T,t)**. Numerical method is based on the results of the analytical **Friedman **method. The results of Friedman Method (curves E(α) and A(α) ) then optimized numerically in order to achieve the better fit between experimental and simulated curves. Calculation of LogA is done for the first order reaction f(alpha)=1-alpha.

The function for optimization is the sum of squares of deviations between measured value Conversion_experimental(T,t) and simulated value Conversion_simulated(T,t). This sum is calculated over all curves and over all points in each curve.

Our numerical method searches numerically values **Ea(alpha)** and **LogA(alpha)** which minimize the optimization function. Internally each point of curves E(α) and A(α) is a subject of small changes, and for each change the sum of the squares of residuals is checked: is it better or worse than before. If better then new point in E(α) or A(α) is saved. The iterations are repeated until no any numerical improvements happens.