Groupe d’études et de recherche en analyse des décisions

Interior point methods: from linear optimization to symmetric optimization

Manuel V. C. Vieira Professeur adjoint, Departamento de Matemática, Universidade Nova de Lisboa, Portugal

We give an introduction to interior point methods for linear optimization.... More specifically, we explain a variant of interior point methods that use kernel functions. We then generalize these methods to symmetric optimization, using tools provided by Euclidean Jordan algebras. A symmetric optimization problem can be defined as minimizing a linear function subject to linear constraints over a symmetric cone.