84 citations · 342 across the 90 of their papers we have counts for
6 papers · 1 filter
Polynomial Template Generation using Sum-of-Squares Programming
Assalé Adjé, Victor Magron
Template abstract domains allow to express more interesting properties than classical abstract domains. However, template generation is a challenging problem when one uses template…
NLCertify: A Tool for Formal Nonlinear Optimization
Victor Magron
NLCertify is a software package for handling formal certification of nonlinear inequalities involving transcendental multivariate functions. The tool exploits sparse semialgebraic…
Error Bounds for Polynomial Optimization over the Hypercube using Putinar type Representations
Victor Magron
Consider the optimization problem , where is a degree multivariate polynomial and is the hypercube. We…
Formal Proofs for Nonlinear Optimization
Victor Magron, Xavier Allamigeon, Stéphane Gaubert +1
We present a formally verified global optimization framework. Given a semialgebraic or transcendental function and a compact semialgebraic domain , we use the nonlinear maxp…
Approximating Pareto Curves using Semidefinite Relaxations
Victor Magron, Didier Henrion, Jean-Bernard Lasserre
We consider the problem of constructing an approximation of the Pareto curve associated with the multiobjective optimization problem $\min_{\mathbf{x} \in \mathbf{S}}\{ (f_1(\mathb…
Certification of Real Inequalities -- Templates and Sums of Squares
Xavier Allamigeon, Stéphane Gaubert, Victor Magron +1
We consider the problem of certifying lower bounds for real-valued multivariate transcendental functions. The functions we are dealing with are nonlinear and involve semialgebraic…