Sensor and actuator placement algorithms are developed for linear discrete-time systems based on H-2 and H-infinity optimization. For sensor placement, we design an observer that minimizes the H-2 norm of the error dynamics and the number of sensors at the same time. For actuator placement, we design a state feedback controller that minimizes the H-infinity norm of the closed-loop system and the number of actuators at the same time. Any other combination of actuator placement for state-feedback design or sensor placement for observer design for continuous-time or discrete-time linear systems based on H-2 or H-infinity optimization can be derived from these results. In both presented cases, the number of sensors or actuators is formulated as the l(0) norm of the observer or controller gain matrix. This l(0) norm is then relaxed to a weighted l(1) norm in order to obtain an iterative convex optimization problem. As an application example, we use the sensor placement algorithm to place phase measurement units with maximal impact on the H-2 performance in a power grid.