Introduction to optimization with applications in astronomy and astrophysics

This chapter aims at providing an introduction to numerical optimizationwith some applications in astronomy and astrophysics. We provide important preliminary definitions that will guide the reader towards differentoptimization procedures. We discuss three families of optimizationproblems and describe numerical algorithms allowing, when this is possible, to solve these problems. For each family, we present in detail simple examples andmore involved advanced examples. As a final illustration, we focus on two worked-out examples of optimization applied to astronomical data. The first application is a supervisedclassification of RR-Lyrae stars. The second one is the denoising of galactic spectraformulated by means of sparsity inducing models in a redundant dictionary.