Direct Search for Linearly Constrained Derivative-Free Optimization

Direct search methods are a popular technique used for derivative-free optimization (DFO). A key benefit of direct search is its flexibility, being suitable for constrained, nonsmooth and mixed integer problems, for example. However, the existing theory for direct search with linear constraints does not allow steps to be taken towards nearby constraints, despite such steps being very helpful in practice. In this talk, I will outline a new convergence theory for direct search, how it justifies these practical choices, and explain the theoretical links to other DFO methods. This is joint work with Clément Royer (U. Paris Dauphine-PSL).