We consider the problem of the optimal selection of a subset of available sensors or actuators in large-scale dynamical systems. By replacing a combinatorial penalty on the number of sensors or actuators with a convex sparsity-promoting term, we cast this problem as a semidefinite program (SDP). The solution of the resulting convex optimization problem is used to select sensors (actuators) in order to gracefully degrade performance relative to the optimal Kalman filter (Linear Quadratic Regulator) that uses all available sensing (actuating) capabilities. Since general-purpose SDP solvers cannot handle typical problem sizes that are of interest in many emerging applications, we employ the proximal gradient method to develop a customized algorithm that is well-suited for large-scale problems. Computational experiments are provided to demonstrate the merits and the effectiveness of our approach. Joint work with Armin Zare and Neil Dhingra