A0512
Title: Contributions of the compositional data methodology to constrained optimization in economics
Authors: Jordi Saperas Riera - Universitat de Girona (Spain) [presenting]
Josep Antoni Martin-Fernandez - University of Girona (Spain)
Abstract: Compositional data provide a specific geometry to the simplex that allows us to study the relationship between the parts of a whole. This geometry is known as Aitchison geometry. The basic operations of Aitchison's geometry defined on the simplex are perturbation and powering. Consequently, the concepts and statistical techniques that are part of the analysis of compositional data must be consistent with Aitchison's geometry. In economics, it is a common problem to look for the distribution of resources that optimizes an indicator or a function. In addition, in many cases, this optimization of resources is conditioned because the variables are constrained. In the modelling of compositional data, we want to make some contributions that allow us to formulate and solve constrained optimization problems, especially convex optimization problems, in a compatible way with Aitchison geometry. To this end, we will define the convex set and convex function in the simplex. Some examples will be presented for illustrating this approach.
