In an optimization process that requires many evaluations of a time-consuming function
\(f\), it can be interesting to build a surrogate model of f, which is a simplified and more time-efficient version of this function. The surrogate model uses the known value of
\(f\) on a set of training points to estimate this function anywhere on its definition space.
The objective of this presentation is to introduce potential uses of surrogate models of objective and constraint functions to improve derivative-free optimization (DFO) methods. In particular, we will consider the following questions:
- What are the different types of surrogate models?
- How can they be used in DFO and, in particular, the MADS (Mesh Adaptive Direct Search) algorithm?
- What are their good and bad properties?
- How do we select the best models to use in a DFO context?