Ana Luísa Custódio (Universidade Nova de Lisboa)

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.