9 citations · 9 across the 9 of their papers we have counts for
9 papers
Sum-of-Squares Certificates for Copositive Matrices via Recursive Identities: The de Klerk-Pasechnik Conjecture and Hoffman-Pereira Matrices
Jineon Baek, Luis Felipe Vargas
We establish the conjecture by de Klerk and Pasechnik (2002), claiming that the semidefinite bounds for the stability number are exact at $r=α(…
Low degree sum-of-squares bounds for the stability number: a copositive approach
Luis Felipe Vargas, Juan C. Vera, Peter J. C. Dickinson
The stability number of a graph , denoted as , is the maximum size of an independent (stable) set in . Semidefinite programming (SDP) methods, which originated from Lov…
On the hardness of deciding the finite convergence of Lasserre hierarchies
Luis Felipe Vargas
A polynomial optimization problem (POP) asks for minimizing a polynomial function given a finite set of polynomial constraints (equations and inequalities). This problem is well-kn…
Copositive matrices, sums of squares and the stability number of a graph
Luis Felipe Vargas, Monique Laurent
This chapter investigates the cone of copositive matrices, with a focus on the design and analysis of conic inner approximations for it. These approximations are based on various s…
Semidefinite approximations for bicliques and biindependent pairs
Monique Laurent, Sven Polak, Luis Felipe Vargas
We investigate some graph parameters dealing with biindependent pairs in a bipartite graph , i.e., pairs where , …
On the Exactness of Sum-of-Squares Approximations for the Cone of Copositive Matrices
Monique Laurent, Luis Felipe Vargas
We investigate the hierarchy of conic inner approximations () for the copositive cone , introduced by Parrilo (Structured Semid…
Exactness of Parrilo's conic approximations for copositive matrices and associated low order bounds for the stability number of a graph
Monique Laurent, Luis Felipe Vargas
De Klerk and Pasechnik (2002) introduced the bounds () for the stability number of a graph and conjectured exactness at order $α(G)…
Minimum cross-entropy distributions on Wasserstein balls and their applications
Luis Felipe Vargas, Mauricio Velasco
Given a prior probability density on a compact set we characterize the probability distribution on contained in a Wasserstein ball centered in a given…
Finite convergence of sum-of-squares hierarchies for the stability number of a graph
Monique Laurent, Luis Felipe Vargas
We investigate a hierarchy of semidefinite bounds for the stability number of a graph , based on its copositive programming formulation and introduce…