Fundamentals of convex optimization for compositional data

• Jordi Saperas Riera ^[1] ; Josep Antoni Martín Fernández ^[1] ; Glòria Mateu Figueras ^[1]
  1. [1] Universitat de Girona

     Universitat de Girona

     Gerona, España

     
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 47, Nº. 2, 2023, págs. 51-60
• Idioma: inglés
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• Resumen

  • 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