13 citations · 27 across the 11 of their papers we have counts for
7 papers
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…
NLCertify: A Tool for Formal Nonlinear Optimization
Victor Magron
NLCertify is a software package for handling formal certification of nonlinear inequalities involving transcendental multivariate functions. The tool exploits sparse semialgebraic…
Error Bounds for Polynomial Optimization over the Hypercube using Putinar type Representations
Victor Magron
Consider the optimization problem , where is a degree multivariate polynomial and is the hypercube. We…
Formal Proofs for Nonlinear Optimization
Victor Magron, Xavier Allamigeon, Stéphane Gaubert +1
We present a formally verified global optimization framework. Given a semialgebraic or transcendental function and a compact semialgebraic domain , we use the nonlinear maxp…
Approximating Pareto Curves using Semidefinite Relaxations
Victor Magron, Didier Henrion, Jean-Bernard Lasserre
We consider the problem of constructing an approximation of the Pareto curve associated with the multiobjective optimization problem $\min_{\mathbf{x} \in \mathbf{S}}\{ (f_1(\mathb…