Chapter 37: Methodologies and Software for Derivative-Free Optimization

Abstract

Derivative-free optimization (DFO) methods [502] are typically considered for the minimization/maximization of functions for which the corresponding derivatives neither are available for use nor can be directly approximated by numerical techniques. Constraints may be part of the problem definition, but, similar to the objective function, it is possible that their derivatives are not available. Problems of this type are common in engineering optimization, where the value of the functions is often computed by simulation and may be subject to statistical noise or other forms of inaccuracy. In fact, expensive function evaluations would prevent approximation of derivatives, and, even when computed, noise would make such approximations less reliable. In the past couple of decades, intense research has resulted in robust and efficient DFO methods, accompanied by convergence theory and numerical implementations.