The Nelder-Mead (NM) "simplex'' algorithm is an almost 50-year-old derivative-free direct search method for nonlinear optimization. To the surprise (and annoyance) of some optimization researchers, it remains widely used by practitioners despite extremely limited convergence theory, a counterexample, known flaws in practice, and the availability of newer direct search methods that come with mathematical guarantees. Is the Nelder-Mead method fated to undergo an inevitable decline, or does it have a useful role to play? This talk will present the speaker's perspective on these questions, along with comments on NM's continuing popularity and a sketch of associated puzzles.
