Abstract : Surrogates have become an important part of recent optimization methods because they allow to deal with expensive functions. This lecture, that was given as part of the SAMCO (Surrogate- Assisted MultiCriteria Optimization) workshop at the Lorentz Center in February 2016, summarizes the different ways in which surrogates can contribute to optimization algorithms. The course is introduced with two naive (not converging) algorithms, stressing the need for controls that ensure a useful contribution of the surrogate to the optimization. Then, a first class of solutions, based on trust regions, is presented. Next, we discuss implementations where surrogates support stochastic optimization algorithms. The third family of approaches is based on surrogates that provide, in addition to a prediction of the objective function, an estimate of the prediction error: this concerns mainly kriging surrogates. The last part of the course touches upon the topic of ensembles of surrogates.
