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

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[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

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A polynomial function f(x) whose minimum is desired.

A P-Compact representation of the set.

First Steps

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Touch up on the Putinar Positivstellensatz and what it means for us.

Why does it work

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Based in S-Procedure, with the Positivstellensatz all about the right representation.

Example

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Code example in SOStools probably worthwhile!

Reference

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SOS tools manual is a good one

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SOS Basics

Global Minimum

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