## Local Minimizers of the Crouzeix Ratio: A Nonsmooth Optimization Case Study

Given a square matrix $A$ and a polynomial $p$, the Crouzeix ratio is the norm of the polynomial on the field of values of $A$ divided by the 2-norm of the matrix $p(A)$. Crouzeix’s conjecture states that the globally minimal value of the Crouzeix ratio is 0.5, regardless of the matrix order and polynomial degree, … Read more