84 citations · 110 across the 9 of their papers we have counts for
10 papers
Volume of quasi-homogeneous sublevel sets: Two linear algebra deterministic algorithms with convergence rates
Didier Henrion, Jean B Lasserre
We consider the problem of computing the Lebesgue volume of the unit sublevel set of a positive quasi-homogeneous polynomial. Pushing the Lebesgue measure of an ambient bounding bo…
Mixtures Closest to a Given Measure: A Semidefinite Programming Approach
Srećko Đurašinović, Jean-Bernard Lasserre, Victor Magron
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settin…
Leveraging Christoffel-Darboux Kernels to Strengthen Moment-SOS Relaxations
Srećko Ðurašinović, Perla Azzi, Jean-Bernard Lasserre +3
The classical Moment-SOS hierarchy allows one to approximate the global minimum of a polynomial optimization problem through semidefinite relaxations of increasing accuracy. For ma…
Rank conditions for exactness of semidefinite relaxations in polynomial optimization
Jean B Lasserre
We consider the Moment-SOS hierarchy in polynomial optimization. We first provide a sufficient condition to solve the truncated K-moment problem associated with a given degree-2n p…
Verifying Properties of Binary Neural Networks Using Sparse Polynomial Optimization
Jianting Yang, Srećko Ðurašinović, Jean-Bernard Lasserre +2
This paper explores methods for verifying the properties of Binary Neural Networks (BNNs), focusing on robustness against adversarial attacks. Despite their lower computational and…
Revisiting semidefinite programming approaches to options pricing: complexity and computational perspectives
Didier Henrion, Felix Kirschner, Etienne de Klerk +3
In this paper we consider the problem of finding bounds on the prices of options depending on multiple assets without assuming any underlying model on the price dynamics, but only…
Semialgebraic Representation of Monotone Deep Equilibrium Models and Applications to Certification
Tong Chen, Jean-Bernard Lasserre, Victor Magron +1
Deep equilibrium models are based on implicitly defined functional relations and have shown competitive performance compared with the traditional deep networks. Monotone operator e…
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…
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…
TSSOS: A Moment-SOS hierarchy that exploits term sparsity
Jie Wang, Victor Magron, Jean-Bernard Lasserre
This paper is concerned with polynomial optimization problems. We show how to exploit term (or monomial) sparsity of the input polynomials to obtain a new converging hierarchy of s…