POEMA Host Institution: Artelys SA, Paris, France
I hold a Bachelor’s degree in mathematics by the University of Guadalajara. Latter on, I obtained a Master’s degree in Computer Science, from the Center for Research in Mathematics (CIMAT) in Guanajuato, Mexico. In my Master’s thesis I worked in optimization with orthogonality constraints. I was interested in the Riemannian approach of optimization over smooth manifolds of matrices. In particular, Riemannian conjugate gradient methods rely on the concept of a vector transport to build the search direction. However, using a change of variable the problem can be transformed into an optimization problem over the Euclidean space, where classical optimization methods can be used. This idea lead to a Transportless Conjugate Gradient for Optimization on Stiefel Manifold, my Master’s thesis.
My interests lie both in real world applications of constrained optimization and in the development of efficient algorithms for mathematical programming. In particular, polynomial optimization demands my attention due to its wide applicability and its good performance in global optimization.
I am participating in POEMA project ESR 15: Polynomial Optimization Techniques for Energy Network Operation and Design. The main expected result during this project is developing novel practical algorithms based on polynomial relaxations for solving mixed-integer nonlinear programs arising in power systems optimization. A good example is the Optimal Power Flow (OPF) problem where the application of the moment-sos approach for global optimization has shown that the OPF can be successfully convexified for instances where semidefinite programming methods are known to have failed.
This project consists in enumerate, prototype and compare various resolution methods for a given problem. The implementation of the chosen solutions strongly demands reliability and numerical efficiency in order to integrate these features into the nonlinear optimization solver Artelys Knitro.
At Artelys, I will be working with a dynamic high-level R&D IT team. However, I will be able to beneficiate of the collaboration with other members of the POEMA network. As planned secondments, this project considers research stays at CNRS (Toulouse, France) working with Professor D. Henrion, and at Tilburg University (Tilburg, The Netherlands) working with Professor E. de Klerk.