Recent research advocates that replacing the periodic communication paradigm by an event-triggered paradigm can have significant benefits for control systems. While in many event-triggered control solutions transmission decisions are based on full state information, in most applications only partial state information is available for feedback (output measurements). Here we propose an optimization-based output-feedback event-triggered solution for linear discrete-time systems which guarantees a performance bound with respect to periodic control, while reducing the communication load. Performance is measured by a quadratic cost. The usefulness of the results is illustrated through a numerical example