LMIs in Control/Click here to continue/Applications of Non-Linear Systems/Global Minimum of Polynomial via SOS Method

[UNDER CONSTRUCTION] - CME

The global minimum of a certain polynomial functions can be found using Sum-of-Squares (SOS) methods. This is a useful starting point to the more-useful but less straightforward issue of local minimums.

Required Data edit

A polynomial function   whose minimum is desired.

The Problem edit

To find the minimum value of  , we suppose that there exists a scalar   such that

 

This is equivalent to determining if   has a SOS representation, since a SOS polynomial is never negative. This becomes an optimization problem by attempting to find the largest possible   such that a representation exists. In other words, the optimization problem becomes

  subject to  

Example edit

Code example in SOStools probably worthwhile!

Reference edit

SOS tools manual is a good one

Related LMIs edit

SOS Basics

Local Minimum is a solid follow-up

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