Direct-Search Methods for Single and Multiobjective
Derivative-Free Optimization: solving difficult problems in an efficient way

Abstract: Noisy functions, conflictual objectives,
expensive function evaluation are some of the difficulties that we face when working in real
applications. Since the 90’s the mathematical optimization community as renewed
its interest in these classes of problems, in particular because convergence
could be established for some of the algorithms which were commonly used in
engineering. In this talk, we will survey the class of directional
Direct-Search Methods (DSM), both for single and multiobjective derivative-free
optimization problems. These algorithms are relatively easy to implement, only
requiring comparisons among objective function values, and being suited for the
optimization of nonsmooth functions. The major drawback of its use is related to
efficiency. We will also describe several techniques which can be used to
improve the performance of these methods, from the use of interpolation models
to the natural algorithmic strategies of parallelization.