12 citations · 35 across the 17 of their papers we have counts for
29 papers
Tractable semidefinite bounds of positive maximal singular values
Victor Magron, Ngoc Hoang Anh Mai, Yoshio Ebihara +1
We focus on computing certified upper bounds for the positive maximal singular value (PMSV) of a given matrix. The PMSV problem boils down to maximizing a quadratic polynomial on t…
Stability Analysis of Recurrent Neural Networks by IQC with Copositive Mutipliers
Yoshio Ebihara, Hayato Waki, Victor Magron +3
This paper is concerned with the stability analysis of the recurrent neural networks (RNNs) by means of the integral quadratic constraint (IQC) framework. The rectified linear unit…
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…
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…
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 $…