92 citations · 246 across the 75 of their papers we have counts for
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Semidefinite geometry of the numerical range
Didier Henrion
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasibl…
POCP: a package for polynomial optimal control problems
Didier Henrion, Jean-Bernard Lasserre, Carlo Savorgnan
POCP is a new Matlab package running jointly with GloptiPoly 3 and, optionally, YALMIP. It is aimed at nonlinear optimal control problems for which all the problem data are polynom…
On semidefinite representations of plane quartics
Didier Henrion
This note focuses on the problem of representing convex sets as projections of the cone of positive semidefinite matrices, in the particular case of sets generated by bivariate pol…
Approximate volume and integration for basic semi-algebraic sets
Didier Henrion, Jean Bernard Lasserre, Carlo Savorgnan
Given a basic compact semi-algebraic set $\K\subset\R^n$, we introduce a methodology that generates a sequence converging to the volume of $\K$. This sequence is obtained from opti…
Nonlinear optimal control synthesis via occupation measures
Didier Henrion, Jean B. Lasserre, Carlo Savorgnan
We consider nonlinear optimal control problems (OCPs) for which all problem data are polynomial. In the first part of the paper, we review how occupation measures can be used to ap…
Detecting rigid convexity of bivariate polynomials
Didier Henrion
Given a polynomial in variables, a symbolic-numerical algorithm is first described for detecting whether the connected component of the pla…