Luis Felipe Vargas

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20212026

most citedFinite convergence of sum-of-squares hierarchies for the stability number of a graph

9 citations · 9 across the 9 of their papers we have counts for

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8 papers · 1 filter

math.OC2026

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 $ϑ^{(r)} (G) (r \geq 0)$ for the stability number $α (G)$ are exact at $r=α(…

math.OC2025

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 $G$ , denoted as $α (G)$ , is the maximum size of an independent (stable) set in $G$ . Semidefinite programming (SDP) methods, which originated from Lov…

math.OC2024

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…

math.OC2023

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…

math.OC2022

On the Exactness of Sum-of-Squares Approximations for the Cone of $5 \times 5$ Copositive Matrices

Monique Laurent, Luis Felipe Vargas

We investigate the hierarchy of conic inner approximations $K_{n}^{(r)}$ ( $r \in N$ ) for the copositive cone $COP_{n}$ , introduced by Parrilo (Structured Semid…

math.OC2021

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 $ϑ^{(r)} (G)$ ( $r \in N$ ) for the stability number $α (G)$ of a graph $G$ and conjectured exactness at order $α(G)…

math.OC2021

Minimum cross-entropy distributions on Wasserstein balls and their applications

Luis Felipe Vargas, Mauricio Velasco

Given a prior probability density $p$ on a compact set $K$ we characterize the probability distribution $q_{δ}^{*}$ on $K$ contained in a Wasserstein ball $B_{δ} (μ)$ centered in a given…

math.OC2021★ 9 cited

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 $ϑ^{(r)} (G)$ for the stability number $α (G)$ of a graph $G$ , based on its copositive programming formulation and introduce…

Sum-of-Squares Certificates for Copositive Matrices via Recursive Identities: The de Klerk-Pasechnik Conjecture and Hoffman-Pereira Matrices

Low degree sum-of-squares bounds for the stability number: a copositive approach

On the hardness of deciding the finite convergence of Lasserre hierarchies

Copositive matrices, sums of squares and the stability number of a graph

On the Exactness of Sum-of-Squares Approximations for the Cone of 5×5 Copositive Matrices

Exactness of Parrilo's conic approximations for copositive matrices and associated low order bounds for the stability number of a graph

Minimum cross-entropy distributions on Wasserstein balls and their applications

Finite convergence of sum-of-squares hierarchies for the stability number of a graph

On the Exactness of Sum-of-Squares Approximations for the Cone of $5 \times 5$ Copositive Matrices