A new methodology to the design of L-Q regulators for continuous-time systems subject to linear state constraints is proposed, consisting of two parts. In the first one, the positive invariance of the polyhedron defined by the constraints in the state space is imposed, guaranteeing thereby that the constraints will not be violated. Furthermore, the admissible constrained controllers are parameterized via the determination of the elements which are fixed in the state feedback matrix. This parameterization enables in a second part the L-Q regulator to be obtained from the solution of a parameter optimization problem subject to linear constraints, for which it is proposed a specialized feasible directions method.