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- Xavier Allamigeon, Stéphane Gaubert, Victor Magron, Benjamin Werner
- MKM/Calculemus/DML
- 2013

The aim of this work is to certify lower bounds for realvalued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The application range for such a tool is widespread; for instance Hales’ proof of Kepler’s conjecture yields thousands of… (More)

- Thomas C. Hales, Mark Adams, +19 authors Roland Zumkeller
- ArXiv
- 2015

This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project. 2010 Mathematics Subject Classification: 52C17

- Victor Magron, George A. Constantinides, Alastair F. Donaldson
- ACM Trans. Math. Softw.
- 2017

Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance, for FPGAs or custom hardware implementations. This problem becomes challenging when the program does not employ solely linear… (More)

- Assalé Adjé, Pierre-Loïc Garoche, Victor Magron
- SAS
- 2015

While abstract interpretation is not theoretically restricted to specific kinds of properties, it is, in practice, mainly developed to compute linear over-approximations of reachable sets, aka. the collecting semantics of the program. The verification of user-provided properties is not easily compatible with the usual forward fixpoint computation using… (More)

- Victor Magron, Xavier Allamigeon, Stéphane Gaubert, Benjamin Werner
- J. Formalized Reasoning
- 2015

Interpretation (VMCAI), volume 3385, pages 21–47, Paris,<lb>France, January 2005. Springer Verlag.<lb>[Ste74] Gilbert Stengle. A nullstellensatz and a positivstellensatz in semial-<lb>gebraic geometry. Mathematische Annalen, 207(2):87–97, 1974.<lb>[WKKM06] Hayato Waki, Sunyoung Kim, Masakazu Kojima, and Masakazu Mu-<lb>ramatsu. Sums of Squares and… (More)

- Victor Magron, Xavier Allamigeon, Stéphane Gaubert, Benjamin Werner
- Math. Program.
- 2015

- Victor Magron
- ICMS
- 2014

NLCertify is a software package for handling formal certification of nonlinear inequalities involving transcendental multivariate functions. The tool exploits sparse semialgebraic optimization techniques with approximation methods for transcendental functions, as well as formal features. Given a box and a transcendental multivariate function as input,… (More)

- Victor Magron
- 2013

- Victor Magron, Didier Henrion, Jean B. Lasserre
- Oper. Res. Lett.
- 2014

We consider the problem of constructing an approximation of the Pareto curve associated with the multiobjective optimization problem minx∈S{(f1(x), f2(x))}, where f1 and f2 are two conflicting polynomial criteria and S ⊂ Rn is a compact basic semialgebraic set. We provide a systematic numerical scheme to approximate the Pareto curve. We start by reducing… (More)

- Assalé Adjé, Pierre-Loïc Garoche, Victor Magron
- ArXiv
- 2015

In order to address the imprecision often introduced by widening operators, policy iteration based on min-computations amounts to consider the characterization of reachable states of a program as an iterative computation of policies, starting from a post-fixpoint. Computing each policy and the associated invariant relies on a sequence of numerical… (More)