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We consider the problem of minimizing a polynomial function on R n , known to be hard even for degree 4 polynomials. Therefore approximation algorithms are of interest. Lasserre [15] and Parrilo [23] have proposed approximating the minimum of the original problem using a hierarchy of lower bounds obtained via semidefinite programming relaxations. We propose… (More)

We consider the problem of global minimization of rational functions on IR n (unconstrained case), and on an open, connected, semi-algebraic subset of IR n , or the (partial) closure of such a set (constrained case). We show that in the univariate case (n = 1), these problems have exact reformulations as semidefinite programming (SDP) problems, by using… (More)

A variety of problems in mathematical calculus can be solved by recursively applying a finite number of rules. Often, a generic solving strategy can be extracted and an interactive exercise system that emulates a tutor can be implemented. In this paper we show how software developed by us can be used to realize this interactivity. In particular, an… (More)

The problem of minimizing a polynomial function in several variables over R n is considered and an algorithm is given. When the polynomial has a minimum the algorithm returns the global minimum and nds at least one point in every connected component of the set of minimizers. A characterization of such points is given. When the polynomial does not have a… (More)

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