Name
Title | ||
|---|---|---|
On computing the distance to stability for matrices using linear dissipative Hamiltonian systems. |
Abstract | ||
|---|---|---|
In this paper, we consider the problem of computing the nearest stable matrix to an unstable one. We propose new algorithms to solve this problem based on a reformulation using linear dissipative Hamiltonian systems: we show that a matrix A is stable if and only if it can be written as A=(J−R)Q, where J=−JT, R⪰0 and Q≻0 (that is, R is positive semidefinite and Q is positive definite). This reformulation results in an equivalent optimization problem with a simple convex feasible set. We propose three strategies to solve the problem in variables (J,R,Q): (i) a block coordinate descent method, (ii) a projected gradient descent method, and (iii) a fast gradient method inspired from smooth convex optimization. These methods require O(n3) operations per iteration, where n is the size of A. We show the effectiveness of the fast gradient method compared to the other approaches and to several state-of-the-art algorithms. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.automatica.2017.07.047 | Automatica |
Keywords | Field | DocType |
Dissipative Hamiltonian systems,Distance to stability,Convex optimization | Gradient method,Discrete mathematics,Gradient descent,Mathematical optimization,Matrix (mathematics),Proximal Gradient Methods,Random coordinate descent,Coordinate descent,Convex optimization,Linear matrix inequality,Mathematics | Journal |
Volume | Issue | ISSN |
85 | 1 | 0005-1098 |
Citations | PageRank | References |
8 | 0.84 | 8 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Nicolas Gillis | 1 | 503 | 39.77 |
| Punit Sharma | 2 | 17 | 3.17 |