Recent progress in unconstrained nonlinear optimization without derivatives

We present an introduction to a new class of derivative free methods for unconstrained optimization. We start by discussing the motivation for such methods and why they are in high demand by practitioners. We then review the past developments in this field, before introducing the features that characterize the newer algorithms. In the context of a trust region framework, we focus on techniques that ensure a suitable ‘geometric quality’ of the considered models. We then outline the class of algorithms based on these techniques, as well as their respective merits. We finally conclude the paper with a discussion of open questions and perspectives.