Optimal sensor selection via proximal optimization algorithms

We consider the problem of optimal sensor selection in large-scale dynamical systems. To address the combinatorial aspect of this problem, we use a suitable convex surrogate for complexity. The resulting non-convex optimization problem fits nicely into a sparsity-promoting framework for the selection of sensors in order to gracefully degrade performance relative to the optimal Kalman filter that uses all available sensors. Furthermore, a standard change of variables can be used to cast this problem as a semidefinite program (SDP). For large-scale problems, we propose a customized proximal gradient method that scales better than standard SDP solvers. While structural features complicate the use of the proximal Newton method, we investigate alternative second-order extensions using the forward-backward quasi-Newton method.