84 citations · 342 across the 90 of their papers we have counts for
11 papers · 1 filter
Local Lipschitz Constant Computation of ReLU-FNNs: Upper Bound Computation with Exactness Verification
Yoshio Ebihara, Xin Dai, Victor Magron +2
This paper is concerned with the computation of the local Lipschitz constant of feedforward neural networks (FNNs) with activation functions being rectified linear units (ReLUs). T…
Certifying ground-state properties of quantum many-body systems
Jie Wang, Jacopo Surace, Irénée Frérot +4
A ubiquitous problem in quantum physics is to understand the ground-state properties of many-body systems. Confronted with the fact that exact diagonalisation quickly becomes impos…
A real moment-HSOS hierarchy for complex polynomial optimization with real coefficients
Jie Wang, Victor Magron
This paper proposes a real moment-HSOS hierarchy for complex polynomial optimization problems with real coefficients. We show that this hierarchy provides the same sequence of lowe…
Symmetry reduction and recovery of trajectories of optimal control problems via measure relaxations
Nicolas Augier, Didier Henrion, Milan Korda +1
We address the problem of symmetry reduction of optimal control problems under the action of a finite group from a measure relaxation viewpoint. We propose a method based on the mo…
Sums of squares certificates for polynomial moment inequalities
Igor Klep, Victor Magron, Jurij Volčič
This paper introduces and develops the algebraic framework of moment polynomials, which are polynomial expressions in commuting variables and their formal mixed moments. Their posi…
Minimal Sparsity for Second-Order Moment-SOS Relaxations of the AC-OPF Problem
Adrien Le Franc, Victor Magron, Jean-Bernard Lasserre +2
AC-OPF (Alternative Current Optimal Power Flow)aims at minimizing the operating costs of a power gridunder physical constraints on voltages and power injections.Its mathematical fo…
Peak Estimation of Time Delay Systems using Occupation Measures
Jared Miller, Milan Korda, Victor Magron +1
This work proposes a method to compute the maximum value obtained by a state function along trajectories of a Delay Differential Equation (DDE). An example of this task is finding…
Convergence rates for sums-of-squares hierarchies with correlative sparsity
Milan Korda, Victor Magron, Rodolfo Rios-Zertuche
This work derives upper bounds on the convergence rate of the moment-sum-of-squares hierarchy with correlative sparsity for global minimization of polynomials on compact basic semi…
Sums of squares representations on singular loci
Ngoc Hoang Anh Mai, Victor Magron
The problem of characterizing a real polynomial as a sum of squares of polynomials on a real algebraic variety dates back to the pioneering work of Hilbert in [Mathematisch…
Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares
Victor Magron, Przemysław Koprowski, Tristan Vaccon
Pourchet proved in 1971 that every nonnegative univariate polynomial with rational coefficients is a sum of five or fewer squares. Nonetheless, there are no known algorithms for co…
State polynomials: positivity, optimization and nonlinear Bell inequalities
Igor Klep, Victor Magron, Jurij Volčič +1
This paper introduces state polynomials, i.e., polynomials in noncommuting variables and formal states of their products. A state analog of Artin's solution to Hilbert's 17th probl…