Open Access Open Access  Restricted Access Subscription or Fee Access

Solving polynomial systems via LMI: worst and best representation matrices

Graziano Chesi


Polynomial systems can be solved via LMI (linear matrix inequality) optimizations by exploiting the SMR (square matricial representation) of polynomials. This paper investigates the worst and best representation matrices obtainable in these LMI optimizations. In particular, it is shown that there always exist representation matrices for which the computation of the sought solutions either cannot be performed or is ill-conditioned. Moreover, it is shown that the best representation matrices for computing the sought solutions can be obtained by adding suitable LMIs, hence preserving the convexity of the optimization.


polynomial system, LMI, convex optimization

Full Text:



  • There are currently no refbacks.

Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.