Hi, this method is usefull for thermodynamic problems related with non-linear optimization. In chemical Engineering, we apply this method for properties calculation and non-linear control optimization. There are many examples of this topic on the web.

Hi, this method belongs to the family of nonlinear multidimensional numerical methods in the framework of nonlinear programming (nonlinear optimization). It is used in many scientific areas for the cases, when the analycal optimization would be difficult or impossible to apply. There are many sources, where this method is accurately explained, for example in nonlinear programming or nonlinear optimization books.

I just published an article in which the NSGA-II algorithm is combined with the Nelder-Mead optimisation to estimate adsorption parameters from ZLC curves.

http://www.sciencedirect.com/science/article/pii/S0009250915000147

The article and a further article using the Nelder-Mead algorithm to do structural optimisation of a microfluidic system is open access and can be found at my Edinburgh Research Explorer site:

http://www.research.ed.ac.uk/portal/en/persons/daniel-friedrich(8c416a2a-d7e4-4cfd-a248-9cdc6ccf3e47)/publications.html

Hello,

I used Nelder-Mead for parameter identification. The parameters were related to kinetic laws (pre-exponential factors, energies of activation) or unknown concentrations of species. In order to enhance the performance of Nelder-Mead, a multistart strategy based on latin hypercube sampling was developed. See my PhD thesis available there : 

https://tel.archives-ouvertes.fr/tel-00564767/document

Hope it helps,

Pierre

Nelder–Mead method  is a commonly used nonlinear optimization technique. It is a heuristic search method that can converge to non-stationary points.

Check this publication "Mathematical and kinetic modeling of biofilm reactor based on ant colony optimization"

Nelder Mead was used as the original optimisation algorithm in GPS-X, a wastewater treatment simulation program. I am not sure if it is still used. It is also used in STOAT, another wastewater treatment program. If the objective function is smooth then other methods may be better, at least as regards computer time.

If you look through the journal Computers & Chemical Engineering you should find more mainstream chemical engineering examples. A web search also finds more examples. Specific books include "Chemical Engineering Dynamics: Modelling with PC Simulation" and "Nonlinear Systems and Optimization for the Chemical Engineer".

Thanks all for your answers.

Each one gave me hints and interesting papers that really helped me to elaborate my exposition about this nonlinear optimization method and its wide application in ChemEng. 

Sincerely, thank you so much.

Blessings!!

Thanks Jeremy Dudley, your answer was the most complete. Thank you so much!!

The Nelder–Mead method is slow and has a convergence order of 1. This means that it is likely to have large termination errors (usually people do not perform an infinite number of iteration steps). It should only be used as a last resort, if everything else fails, and even then it should be followed up with a Marquardt–Levenberg or Powell algorithm.

The Nelder–Mead method may be advantageous if the object function is noisy (cannot be computed with sufficient accuracy to obtain local gradients) or if the number of optimizable parameters is very large.

Thanks Ulrich!