Simplex-Levenberg-Marquardt method

The numerical parameter estimation was based on kinetic experiments out of which the temperatures and concentrations were recorded for the compounds. The kinetic and adsorption parameters were estimated by using the Simplex-Levenberg-Marquardt method, which minimizes the residual sum of squares between the estimated and the experimental concentrations with non-linear regression. 

The weighted sum of squares between measured and estimated concentrations was minimized by a hybrid simplex-Levenberg-Marquardt algorithm implemented in the simulation software Modest (Haario 1994). The model equations were solved in situ during the parameter estimation by the backward difference method. The estimated parameters were the kinetic and adsorption equilibrium constants of the system. The simulation results revealed that the model was able to describe the behaviour of the system. The parameter values were reasonable and comparable with values obtained in previous studies concerning citral hydrogenation in a slurry reactor (Tiainen 1998). 

Various optimum search methods exist for the minimization of objective functions, which can be used for the estimation of kinetic constants [3], for example, the Fibonacci method, the golden section method, the Newton-Raphson method, the Levenberg-Marquardt method, and the simplex method. Recently, even genetic algorithms have been... 

Commercially available software developed to process individual impedance spectra use few general algorithms such as Levenberg-Marquardt algorithm, the Nelder-Mead downhill simplex method or genetic algorithms [3-7]. The software is optimized to process only... 

---