3 papers
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.AG2023
Sum-of-squares certificates for copositivity via test states
Markus Schweighofer, Luis Felipe Vargas
In 1995, Reznick showed an important variant of the obvious fact that any positive semidefinite (real) quadratic form is a sum of squares of linear forms: If a form (of arbitrary e…
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…