Discussing the article: "Population optimization algorithms: Nelder–Mead, or simplex search (NM) method"
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Check out the new article: Population optimization algorithms: Nelder–Mead, or simplex search (NM) method.
The article presents a complete exploration of the Nelder-Mead method, explaining how the simplex (function parameter space) is modified and rearranged at each iteration to achieve an optimal solution, and describes how the method can be improved.
The Nelder-Mead method was developed in 1965 by John Nelder and Roger Mead. They were looking for an optimization method that could work with functions that did not have derivatives or did not have analytical equations for derivatives. They also wanted to develop a method that would be easy to implement and efficient for use on the computing machines of the day. The research led them to the idea of using a simplex - a polyhedron in the space of function parameters.
The history of the method's creation began with the work of John Nelder and his colleagues at the Computing Laboratory in Oxford. They were faced with the problem of optimizing functions that did not have analytical derivatives or were too complex to calculate. Traditional optimization methods such as gradient methods were not applicable in such cases. Instead, Nelder and Mead proposed a new method based on iteratively searching for the optimal solution in the space of the function parameters.
The Nelder-Mead method was called the "simplex method" and was published in the article "A Simplex Method for Function Minimization" in The Computer Journal in 1965. This method has been accepted by the scientific community and has become widely used in various fields requiring function optimization.
A simplex is a set of points forming a polyhedron, where each point is a set of parameter values of the function being optimized. The idea is to change and move the simplex in the parameter space to find the optimal value of the function.
Author: Andrey Dik