Positivity certificates by sums of squares
Certify polynomial non-negativity with semidefinite programming and convert numerical certificates into exact rational ones.
- Suitable for
- Master's thesis
- Supervision
- Tülay Ayyıldız
- Prerequisites
- Linear algebra; convex optimization basics
A polynomial that is a sum of squares is non-negative, and sums-of-squares decompositions can be found by semidefinite programming. The numerical output, however, is only approximate.
Goal
Compute sums-of-squares decompositions numerically, round and project them to exact rational certificates, and study when this succeeds.