84 citations · 342 across the 90 of their papers we have counts for
8 papers · 1 filter
Time-dependent moments from partial differential equations and the time-dependent set of atoms
Raúl E. Curto, Philipp J. di Dio, Milan Korda +1
We study the time-dependent moments and associated polynomials arising from the partial differential equation , and consider in deta…
Exploiting ideal-sparsity in the generalized moment problem with application to matrix factorization ranks
Milan Korda, Monique Laurent, Victor Magron +1
We explore a new type of sparsity for the generalized moment problem (GMP) that we call ideal-sparsity. This sparsity exploits the presence of equality constraints requiring the me…
Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant
Ngoc Hoang Anh Mai, Victor Magron, Jean-Bernard Lasserre +1
We consider polynomial optimization problems (POP) on a semialgebraic set contained in the nonnegative orthant (every POP on a compact set can be put in this format by a simple tra…
Sparse Polynomial Optimization: Theory and Practice
Victor Magron, Jie Wang
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can conv…
Urysohn in action: separating semialgebraic sets by polynomials
Milan Korda, Jean-Bernard Lasserre, Alexey Lazarev +2
A classical result from topology called Uryshon's lemma asserts the existence of a continuous separator of two disjoint closed sets in a sufficiently regular topological space. In…
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…
Exact SOHS decompositions of trigonometric univariate polynomials with Gaussian coefficients
Victor Magron, Mohab Safey El Din, Markus Schweighofer +1
Certifying the positivity of trigonometric polynomials is of first importance for design problems in discrete-time signal processing. It is well known from the Riesz-Fejéz spectral…