Vladimir Protasov – Optimization Online

Computing closest stable non-negative matrices

Published: 2017/08/24

Convex and Nonsmooth Optimization distance to infeasibility, non-negative matrix, polyhedral norm, schur stability, spectral radius

Problem of finding the closest stable matrix for a dynamical system has many applications. It is well studied both for continuous and discrete-time systems, and the corresponding optimization problems are formulated for various matrix norms. As a rule, non-convexity of these formulations does not allow finding their global solutions. In this paper, we analyze positive … Read more

Optimizing the Spectral Radius

Published: 2011/12/12, Updated: 2012/07/08

Yurii Nesterov

Vladimir Protasov

Control Applications nonnegative matrix, optimization methods, spectral radius, spectrum of a graph

We suggest an approach for finding the maximal and the minimal spectral radius of linear operators from a given compact family of operators, which share a common invariant cone (e.g. for a family of nonnegative matrices). In case of families with so-called product structure, this leads to efficient algorithms for optimizing the spectral radius and … Read more