Solving polynomial systems via LMI: determination of optimal SMR matrices
by
Graziano Chesi
University of Hong Kong

LMI can be useful for solving systems of polynomial equations and inequalities provided that the dimension of the null-space of some representation matrices obtained in the LMI optimization is smaller than a certain threshold. In this talk we show that, unfortunately, there always exist such representation matrices for which this dimension is larger than the allowed threshold or for which the computation of the null-space required to extract the sought solution is arbitrarily ill-conditioned. In order to solve these problems we propose a strategy based on a finite sequence of LMI optimizations for computing the representation matrices with the smallest null-space and with large condition numbers.

Date received: March 14, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawz-32.