Pre- and post-processing sum-of-squares programs in practice

Abstract—Checking non-negativity of polynomials using sum-of-squares has recently been popularized and found many applications in control. Although the method is based on convex programming, the optimization problems rapidly grow and result in huge semidefinite programs. Addi-tionally, they often become increasingly ill-conditioned. To alleviate these problems, it is important to exploit properties of the analyzed polynomial, and post-process the obtained solution. This technical note describes how the sum-of-squares module in the MATLAB toolbox YALMIP handles these issues. Index Terms—Optimization methods, polynomials, software packages. I