84 citations · 342 across the 90 of their papers we have counts for
7 papers · 1 filter
On Exact Reznick, Hilbert-Artin and Putinar's Representations
Victor Magron, Mohab Safey El Din
We consider the problem of computing exact sums of squares (SOS) decompositions for certain classes of non-negative multivariate polynomials, relying on semidefinite programming (S…
In SDP relaxations, inaccurate solvers do robust optimization
Jean-Bernard Lasserre, Victor Magron
We interpret some wrong results (due to numerical inaccuracies) already observed when solving SDP-relaxations for polynomial optimization on a double precision floating point SDP s…
Semidefinite Approximations of Invariant Measures for Polynomial Systems
Victor Magron, Marcelo Forets, Didier Henrion
We consider the problem of approximating numerically the moments and the supports of measures which are invariant with respect to the dynamics of continuous- and discrete-time poly…
RealCertify: a Maple package for certifying non-negativity
Victor Magron, Mohab Safey El Din
Let (resp. ) be the field of rational (resp. real) numbers and be variables. Deciding the non-negativity of polynomials in $\mathb…
On Exact Polya and Putinar's Representations
Victor Magron, Mohab Safey El Din
We consider the problem of finding exact sums of squares (SOS) decompositions for certain classes of non-negative multivariate polynomials, relying on semidefinite programming (SDP…
Certified Roundoff Error Bounds using Bernstein Expansions and Sparse Krivine-Stengle Representations
Victor Magron, Alexandre Rocca, Thao Dang
Floating point error is a drawback of embedded systems implementation that is difficult to avoid. Computing rigorous upper bounds of roundoff errors is absolutely necessary for the…
Optimal data fitting: a moment approach
Jean-Bernard Lasserre, Victor Magron
We propose a moment relaxation for two problems, the separation and covering problem with semi-algebraic sets generated by a polynomial of degree d. We show that (a) the optimal va…