84 citations · 342 across the 90 of their papers we have counts for
14 papers · 1 filter
Exploiting Term Sparsity in Moment-SOS hierarchy for Dynamical Systems
Jie Wang, Corbinian Schlosser, Milan Korda +1
In this paper, we develop a dynamical system counterpart to the term sparsity sum-of-squares (TSSOS) algorithm proposed for static polynomial optimization. This allows for computat…
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…
Noncommutative Polynomial Optimization
Abhishek Bhardwaj, Igor Klep, Victor Magron
In this chapter we present the sums of Hermitian squares approach to noncommutative polynomial optimization problems. This is an extension of the sums of squares approach for polyn…
Certifying Global Optimality of AC-OPF Solutions via sparse polynomial optimization
Jie Wang, Victor Magron, Jean B. Lasserre
We report the experimental results on certifying 1% global optimality of solutions of AC-OPF instances from PGLiB via the CS-TSSOS hierarchy -- a moment-SOS based hierarchy that ex…
Dimension-free entanglement detection in multipartite Werner states
Felix Huber, Igor Klep, Victor Magron +1
Werner states are multipartite quantum states that are invariant under the diagonal conjugate action of the unitary group. This paper gives a complete characterization of their ent…
Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients
Victor Magron, Mohab Safey El Din, Trung-Hieu Vu
Assessing non-negativity of multivariate polynomials over the reals, through the computation of {\em certificates of non-negativity}, is a topical issue in polynomial optimization.…
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…
Noncommutative Christoffel-Darboux Kernels
Serban T. Belinschi, Victor Magron, Victor Vinnikov
We introduce from an analytic perspective Christoffel-Darboux kernels associated to bounded, tracial noncommutative distributions. We show that properly normalized traces, respecti…
On the complexity of Putinar-Vasilescu's Positivstellensatz
Ngoc Hoang Anh Mai, Victor Magron
We provide a new degree bound on the weighted sum-of-squares (SOS) polynomials for Putinar-Vasilescu's Positivstellensatz. This leads to another Positivstellensatz saying that if $…
Exploiting Sparsity in Complex Polynomial Optimization
Jie Wang, Victor Magron
In this paper, we study the sparsity-adapted complex moment-Hermitian sum of squares (moment-HSOS) hierarchy for complex polynomial optimization problems, where the sparsity includ…
TSSOS: a Julia library to exploit sparsity for large-scale polynomial optimization
Victor Magron, Jie Wang
The Julia library TSSOS aims at helping polynomial optimizers to solve large-scale problems with sparse input data. The underlying algorithmic framework is based on exploiting corr…
The Constant Trace Property in Noncommutative Optimization
Ngoc Hoang Anh Mai, Abhishek Bhardwaj, Victor Magron
In this article, we show that each semidefinite relaxation of a ball-constrained noncommutative polynomial optimization problem can be cast as a semidefinite program with a constan…
A Sublevel Moment-SOS Hierarchy for Polynomial Optimization
Tong Chen, Jean-Bernard Lasserre, Victor Magron +1
We introduce a sublevel Moment-SOS hierarchy where each SDP relaxation can be viewed as an intermediate (or interpolation) between the d-th and (d+1)-th order SDP relaxations of th…
Stability of Linear Systems under Extended Weakly-Hard Constraints
Nils Vreman, Paolo Pazzaglia, Jie Wang +2
Control systems can show robustness to many events, like disturbances and model inaccuracies. It is natural to speculate that they are also robust to sporadic deadline misses when…