Minimum Ellipsoid Bounds for Solutions of Polynomial Systems via Sum of Squares

Authors:
Jiawang Nie;James W. Demmel
Affiliations:
Department of Mathematics, University of California, Berkeley, USA 94720;Department of Mathematics and EECS, University of California, Berkeley, USA 94720
Venue:
Journal of Global Optimization
Year:
2005

Citing 4
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Ellipsoidal bounds for uncertain linear equations and dynamical systems

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Duality of Ellipsoidal Approximations via Semi-Infinite Programming

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Abstract

We study ellipsoid bounds for the solutions $$(x,\mu) \in \mathbb{R}^{n} \times \mathbb{R}^{r}$$ of polynomial systems of equalities and inequalities. The variable 驴 can be considered as parameters perturbing the solution x. For example, bounding the zeros of a system of polynomials whose coefficients depend on parameters is a special case of this problem. Our goal is to find minimum ellipsoid bounds just for x. Using theorems from real algebraic geometry, the ellipsoid bound can be found by solving a particular polynomial optimization problem with sums of squares (SOS) techniques. Some numerical examples are also given.