Polynomial Root Radius Optimization with Affine Constraints

The root radius of a polynomial is the maximum of the moduli of its roots (zeros). We consider the following optimization problem: minimize the root radius over monic polynomials of degree $n$, with either real or complex coefficients, subject to $k$ consistent affine constraints on the coefficients. We show that there always exists an optimal … Read more

Variational Analysis of the Spectral Abscissa at a Matrix with a Nongeneric Multiple Eigenvalue

The spectral abscissa is a fundamental map from the set of complex matrices to the real numbers. Denoted $\alpha$ and defined as the maximum of the real parts of the eigenvalues of a matrix $X$, it has many applications in stability analysis of dynamical systems. The function $\alpha$ is nonconvex and is non-Lipschitz near matrices … Read more