Luis Felipe Vargas

I am a Postdoctoral Researcher in the group of Optimization 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 (SNSF)

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 Bit Size of Sum-of-Squares Proofs for Symmetric Formulations. With Alex Bortolotti, Monaldo Mastrolilli and Marilena Palomba. Preprint at arXiv, 2025.
Low degree sum-of-squares bounds for the stability number: a copositive approach. With Juan C. Vera and Peter Dickinson arXiv, 2025.
On the Degree Automatability of Sum-of-Squares Proofs. With Alex Bortolotti and Monaldo Mastrolilli. Preprint at arXiv, 2025.
Computational complexity of sum-of-squares bounds for copositive programs. With Marilena Palomba, Lucas Slot and Monaldo Mastrolilli. Preprint at arXiv, 2025.
Sum-of-squares certificates for copositivity via test states. with Markus Schweighofer. SIAM Journal on Applied Algebra and Geometry, 8(4): 797-820. Preprint at arXiv, 2024.
On the hardness of deciding the finite convergence of Lasserre hierarchies. Numerical Algebra, Control and Optimization (NACO), Paper, Preprint at arXiv, 2024.
Semidefinite bounds for bicliques and biindependent pairs. With Monique Laurent and Sven Polak. Preprint at arXiv. Accepted for publication in Mathematics of Operations Research, published online, 2024.
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

my thesis is available online

Luis Felipe Vargas

Publications and Preprints

Theses