Optimizing the spectral radius (Q2866221)

The authors propose an approach to finding the maximal and the minimal spectral radii of finite-dimensional linear operators from some compact family. All the operators share a common invariant cone, which is supposed to be convex, closed, solid, and pointed. A special attention is given to the so-called product families. In this case, two methods for maximizing the spectral radius of product families are developed. A particular case has been considered by \textit{V. D. Blondel} and \textit{Yu. Nesterov} [SIAM J. Matrix Anal. Appl. 31, No. 3, 865--876 (2009; Zbl 1201.65051)]. In the end, two applications are discussed: one deals with non-stationary difference equations and the other consists in optimizing the spectral radius of the adjacency matrix of a graph.