By Topic

Tightness Conditions for Semidefinite Relaxations of Forms Minimization

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Chesi, G. ; Dept. of Electr. & Electron. Eng., Univ. of Hong Kong, Hong Kong

The Gram matrix allows to compute a lower bound of the minimum of a form via an LMI (linear matrix inequality) optimization by exploiting SOS (sum of squares) relaxations. This paper introduces and characterizes the Gram-tight forms, i.e. forms whose minimum coincides with this lower bound. In particular, it is shown that one can establish that a form is Gram-tight just by checking whether the dimension of the null space of the matrix returned by the LMI solver belongs to a certain range. This fact is not only theoretically interesting but has also useful applications as shown by examples with uncertain systems and nonlinear systems.

Published in:

Circuits and Systems II: Express Briefs, IEEE Transactions on  (Volume:55 ,  Issue: 12 )