Noncommutative Polynomial Optimization

TL;DR

This paper introduces a method for optimizing noncommutative polynomials using sums of Hermitian squares, extending classical algebraic techniques to noncommutative settings with theoretical insights.

Contribution

It extends the sums of squares approach from real algebraic geometry to noncommutative polynomial optimization, providing foundational theory and highlighting its significance.

Findings

Framework for noncommutative polynomial optimization

Extension of sums of squares methodology

Theoretical foundation for practical applications

Abstract

In this chapter we present the sums of Hermitian squares approach to noncommutative polynomial optimization problems. This is an extension of the sums of squares approach for polynomial optimization arising from real algebraic geometry. We provide a gentle introduction to the underlying theory of this methodology and highlight its importance.