Implementing the Nelder‐Mead simplex algorithm with adaptive parameters

In this paper, we first prove that the expansion and contraction steps of the Nelder‐Mead simplex algorithm possess a descent property when the objective function is uniformly convex. This property provides some new insights on why the standard Nelder‐Mead algorithm becomes inefficient in high dimensions. We then propose an implementation of the Nelder‐Mead method in which the expansion, contraction, and shrink parameters depend on the dimension of the optimization problem. Our numerical experiments show that the new implementation outperforms the standard Nelder‐Mead method for high dimensional problems.