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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)

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)

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)

We consider here the problem of minimizing a polynomial function on R n. The problem is known to be hard even for degree 4. Therefore approximation algorithms are of interest. Lasserre [11] and Parrilo [16] have proposed approximating the minimum of the original problem using a hierarchy of lower bounds obtained via semidefi-nite programming relaxations. We… (More)

- Dorina Jibetean
- 2001

The paper deals with unconstrained global minimization of rational functions. A necessary condition is given for the function to have a nite innmum. In case the condition is satissed, the problem is shown to be equivalent to a speciic constrained polynomial optimization problem. In this paper, we solve a relaxation of the latter formulation using… (More)

- A. M. Cohen, H. Cuypers, E. Reinaldo Barreiro, Manfred Riem, Olga Caprotti, Hans Sterk +3 others
- 2005

This section deals with our work on interactive mathematical documents that make use of the World Wide Web. These documents take input from various sources, users, and mathematical services. Communication between these different entities can be realized using OpenMath. But, such communication and the interactivity inside the mathematical document take place… (More)

In this paper we study unconstrained global optimization of rational functions. We give first few theoretical results and study then a relaxation of the initial problem. The relaxation is solved using LMI techniques. Therefore, in general our procedure will produce a lower bound of the infimum of the original problem. However, under no degeneracies, it is… (More)

A state-space approach to H 2 model reduction of stable systems is pursued, using techniques from global rational optimization , and aimed at finding global optima. First, a concentrated version of the H 2 criterion is derived, by optimizing analytically with respect to a subset of parameters. Next, a bound is developed, which is shown to be sharp for… (More)

A method is described for finding the global minimum or infimum of a polynomial in several variables. Both the value of the minimum or infimum is obtained as well as at least one point where the minimum is attained if it is attained. If the minimum is attained in finitely many points, the method finds them all. The method is based on the Stetter–Möller… (More)