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Minimum Ellipsoid Bounds for Solutions of Polynomial Systems via Sum of Squares | | Jiawang Nie
; James W. Demmel
; | | Date: |
5 Nov 2004 | | Subject: | Optimization and Control | math.OC | | Abstract: | We study ellipsoid bounds for the solutions $(x,mu)in
e^n imes
e^r$ of polynomial systems of equalities and inequalities. The variable $mu$ 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. | | Source: | arXiv, math.OC/0411122 | | Services: | Forum | Review | PDF | Favorites | |
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