Algebraic Relaxations and Hardness Results in Polynomial Optimization and Lyapunov Analysis

TL;DR

This thesis explores the computational complexity and algebraic relaxations in polynomial optimization and Lyapunov analysis, providing new insights into their limitations and capabilities.

Contribution

It offers new hardness results and algebraic relaxation techniques for polynomial optimization and control problems.

Findings

Establishes new computational hardness results.

Develops algebraic relaxation methods.

Analyzes limitations of semidefinite programming relaxations.

Abstract

This thesis settles a number of questions related to computational complexity and algebraic, semidefinite programming based relaxations in optimization and control.