The use of optimization is an alternative to the well-known automatic PID tuning rules. However, for a proper approach to the optimization problem, the stability of the resulting closed-loop must be guaranteed. A framework for the PID parameter optimization, with stability guarantees, is proposed in this paper. The framework is intended to be used to refine an initial choice for the PID parameters. The way to the solution is based on to the characterization of the set of PID achievable designs and the establishment of a condition that will ensure us to move on to the appropriate subset of achievable stable PID designs. The optimization procedure is applied to tune a PI controller on an unstable system and also on a non-minimum phase system.