84 citations · 342 across the 90 of their papers we have counts for
15 papers · 1 filter
Exploiting constant trace property in large-scale polynomial optimization
Ngoc Hoang Anh Mai, Jean-Bernard Lasserre, Victor Magron +1
We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matri…
Minimizing rational functions: a hierarchy of approximations via pushforward measures
Jean Bernard Lasserre, Victor Magron, Swann Marx +1
This paper is concerned with minimizing a sum of rational functions over a compact set of high-dimension. Our approach relies on the second Lasserre's hierarchy (also known as the…
SONC Optimization and Exact Nonnegativity Certificates via Second-Order Cone Programming
Victor Magron, Jie Wang
The second-order cone (SOC) is a class of simple convex cones and optimizing over them can be done more efficiently than with semidefinite programming. It is interesting both in th…
Induced Norm Analysis of Discrete-Time LTI Systems for Nonnegative Input Signals and Its Application to Stability Analysis of Recurrent Neural Networks
Yoshio Ebihara, Hayato Waki, Victor Magron +3
In this paper, we focus on the "positive" induced norm of discrete-time linear time-invariant systems where the input signals are restricted to be nonnegative. To cope with t…
Exploiting term sparsity in Noncommutative Polynomial Optimization
Jie Wang, Victor Magron
We provide a new hierarchy of semidefinite programming relaxations, called NCTSSOS, to solve large-scale sparse noncommutative polynomial optimization problems. This hierarchy feat…
Correlations constrained by composite measurements
John H. Selby, Ana Belén Sainz, Victor Magron +2
How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpo…
SparseJSR: A Fast Algorithm to Compute Joint Spectral Radius via Sparse SOS Decompositions
Jie Wang, Martina Maggio, Victor Magron
This paper focuses on the computation of joint spectral radii (JSR), when the involved matrices are sparse. We provide a sparse variant of the procedure proposed by Parrilo and Jad…
A hierarchy of spectral relaxations for polynomial optimization
Ngoc Hoang Anh Mai, Victor Magron, Jean-Bernard Lasserre
We show that (i) any constrained polynomial optimization problem (POP) has an equivalent formulation on a variety contained in an Euclidean sphere and (ii) the resulting semidefini…
Optimization over trace polynomials
Igor Klep, Victor Magron, Jurij Volčič
Motivated by recent progress in quantum information theory, this article aims at optimizing trace polynomials, i.e., polynomials in noncommuting variables and traces of their produ…
Computer-assisted proofs for Lyapunov stability via Sums of Squares certificates and Constructive Analysis
Grigory Devadze, Victor Magron, Stefan Streif
We provide a computer-assisted approach to ensure that a given continuous or discrete-time polynomial system is (asymptotically) stable. Our framework relies on constructive analys…
CS-TSSOS: Correlative and term sparsity for large-scale polynomial optimization
Jie Wang, Victor Magron, Jean B. Lasserre +1
This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-scale sparse polynomial optimization problems. Its novelty is to exploit simultaneously correlativ…
Chordal-TSSOS: a moment-SOS hierarchy that exploits term sparsity with chordal extension
Jie Wang, Victor Magron, Jean-Bernard Lasserre
This work is a follow-up and a complement to arXiv:1912.08899 [math.OC] for solving polynomial optimization problems (POPs). The chordal-TSSOS hierarchy that we propose is a new sp…
A sparse version of Reznick's Positivstellensatz
Ngoc Hoang Anh Mai, Victor Magron, Jean-Bernard Lasserre
If is a positive definite form, Reznick's Positivstellensatz [Mathematische Zeitschrift. 220 (1995), pp. 75--97] states that there exists such that ${\| x \|^{…
Semialgebraic Optimization for Lipschitz Constants of ReLU Networks
Tong Chen, Jean-Bernard Lasserre, Victor Magron +1
The Lipschitz constant of a network plays an important role in many applications of deep learning, such as robustness certification and Wasserstein Generative Adversarial Network.…
Computing the Hausdorff boundary measure of semi-algebraic sets
Jean-Bernard Lasserre, Victor Magron
Given a compact basic semi-algebraic set we provide a numerical scheme to approximate as closely as desired, any finite number of moments of the Hausdorff measure on the boundary o…