15h30 - 17h10
Blackbox and derivative-free optimization
Some problems do not possess the required structure to be addressed by traditional optimization methods. In this presentation, we focus on situations where the evaluation of the functions to be minimized and those delimiting the feasible region are assessed by running a computer simulation, expensive in terms of computational time, and for which derivatives are either inexistant or unavailable. These functions are usually nonsmooth, discontinuous, and may even be contaminated by numerical noise.
The tutorial follows the structure of our recent textbook on the subject (Springer Series in Operations Research and Financial Engineering, 2017). We present a brief history of direct-search methods designed for these blackbox and derivative-free optimization problems, and their convergence analysis using nonsmooth calculus. We also discuss the construction of linear and quadratic models, and how to integrate them into linesearch or trust-region methods. We will also discuss recent developments and extensions including including the use of surrogates and strategies to handle various types of constraints, as well as selected applications from engineering.
This tutorial is intended for anyone interested in blackbox or derivative-free optimization. We do not present the absolute state-of-the-art in modern algorithms and theory, as we feel that it belongs to the specialized sessions of the conference.