Abstract
The objective of the paper is to investigate relationships among different convex relaxations for quadratic distance problems. The main motivation is that a number of problems in robust control can be cast as minimum distance problems from a point to a polynomial surface. It is proven that two families of relaxations proposed in the literature, both based on sum of squares, are equivalent: the former exploits properties of homogeneous forms, while the latter relies on the Positivstellensatz theorem. It is also shown that two different relaxations based on Positivstellensatz present different levels of conservativeness. The results presented in the paper provide useful insights on the trade off between computational burden and conservativeness of the considered relaxations.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
