Luis Felipe Vargas
I am a Postdoctoral Researcher in the group of Algorithms and Complexity at Istituto Dalle Molle di Studi sull'Intelligenza Artificiale (IDSIA), USI - SUPSI, in Lugano, Switzerland.
I work in the project "Ideal Membership Problems and the Bit Complexity of Sum of Squares Proofs" supported by the Swiss National Science Foundation (SCNF)
Previously, I was a PhD student at Centrum Wiskunde & Informatica (CWI, Amsterdam) in the Networks & Optimization group, under the supervision of Monique Laurent. I defended my thesis cum laude at Tilburg University on 3 November 2023.
I obtained my MSc (and Bsc) in Mathematics at Universidad de los Andes working with Mauricio Velasco (and Guillermo Mantilla).
email: luis (dot) vargas (at) idsia (dot) ch
Publications and Preprints
On the hardness of deciding the finite convergence of Lasserre hierarchies. Numerical Algebra, Control and Optimization (NACO), Paper, Preprint at arXiv, 2024.
Sum-of-squares certificates for copositivity via test states. with Markus Schweighofer. Preprint at arXiv, 2023.
Semidefinite bounds for bicliques and biindependent pairs. With Monique Laurent and Sven Polak. Mathematics of Operations Research, published online, 2024. Preprint at arXiv.
Copositive matrices, sums of squares and the stability number of a graph. With Monique Laurent. Preprint at arXiv. In: Polynomial Optimization, Moments, and Applications. M. Kocvara, B. Mourrain, C. Riener (eds). Springer Optimization and Its Applications (SOIA, volume 206), pages 99--132, 2023.
On the exactness of sum-of-squares approximations for the cone of 5x5 copositive matrices. With Monique Laurent. Linear Algebra and its Applications, 651:26-50, 2022. Paper and Preprint at arXiv.
Exactness of Parrilo's conic approximations for copositive matrices and associated low order bounds for the stability number of a graph. With Monique Laurent. Mathematics of Operations Research, 48(2):1017--1043, 2022. Paper and preprint at arXiv.
- Finite convergence of sum-of-squares hierarchies for the stability number of a graph. With Monique Laurent. SIAM Journal on Optimization, 32(2):491--518, 2022. Preprint at arXiv.
- Minimum cross-entropy distributions on Wasserstein balls and their applications. with Mauricio Velasco, https://arxiv.org/abs/2106.03226, 2021
