Resumen de Fundamentals of convex optimization for compositional data

Jordi Saperas Riera, Josep Antoni Martín Fernández , Glòria Mateu Figueras

• Many of the most popular statistical techniques incorporate optimisation problems in their inner workings. A convex optimisation problem is defned as the problem of min- imising a convex function over a convex set. When traditional methods are applied to compositional data, misleading and incoherent results could be obtained. In this paper, we fll a gap in the specialised literature by introducing and rigorously defning novel con- cepts of convex optimisation for compositional data according to the Aitchison geometry.

  Convex sets and convex functions on the simplex are defned and illustrated