We consider the class of nonlinear optimal control problems with all data (differentail equation, state and control constraints, cost) being polynomials. We provide a simple hierarchy of… (More)

This paper presents necessary and suucient conditions for the existence of solutions to cone-constrained linear equations in some function spaces. These conditions yield, in particular, the classical… (More)

We investigate and discuss when the inverse of a multivariate truncated moment matrix has zeros in some prescribed entries. We find that the key factor behind that property is a certain conditional… (More)

We consider the semi-infinite optimization problem: f := min x∈X {f(x) : g(x,y) ≤ 0, ∀y ∈ Yx }, where f, g are polynomials and X ⊂ R as well as Yx ⊂ R , x ∈ X, are compact basic semi-algebraic sets.… (More)

We consider the integer program max{c′x |Ax = b, x ∈ Nn}. A formal parallel between linear programming and continuous integration, and discrete summation, shows that a natural duality for integer… (More)

Let V ⊂R<sup>n</sup>be a real algebraic set described by finitely many polynomials equations g<inf>j</inf>(x)=0, j∈J, and let f be a real polynomial, nonnegative on V. We show that for… (More)

In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is finte. The aim is to combine approaches for solving a… (More)