LMIs in Control/Click here to continue/Applications of Non-Linear Systems/Local Minimum of Polynomial via SOS Method
[UNDER CONSTRUCTION] - CME
The local minimum of a certain polynomial functions f(x) can be found using Sum-of-Squares (SOS) methods. Here we assume the local set has a P-Compact representation, and that this representation is used.
Required Data edit
A polynomial function f(x) whose minimum is desired.
A P-Compact representation of the set.
First Steps edit
Touch up on the Putinar Positivstellensatz and what it means for us.
Why does it work edit
Based in S-Procedure, with the Positivstellensatz all about the right representation.
Example edit
Code example in SOStools probably worthwhile!
Reference edit
SOS tools manual is a good one
Related LMIs edit
SOS Basics
Global Minimum