This paper is intended not as a survey, but as an introduction to some ideas behind the class of mesh adaptive direct search (MADS) methods. Space limitations dictate a brief description of various key topics be provided along with several references, which themselves provide further references.

The convergence theory for the methods presented here make a case for closing the gap between nonlinear optimizers and nonsmooth analysts. However these methods are certainly not of purely theoretical interest; they are successful on difficult practical problems. To encourage further use, we give references to available implementations. MADS is implemented in the direct search portion of the MathWorks MATLAB Ge- netic Algorithm and Direct Search (GADS) Toolbox.