This paper deals with the problem of constrained optimization in dynamic linear time-invariant (LTI) systems characterized by a control vector dimension less than that of the system state vector. The problem consists in designing a control signal capable of generating a system state evolution confined to the feasible region delimited by a number of inequality constraints less than or equal to the number of control vector components, as well as of steering the state trajectory to an equilibrium point where a prespecified cost function depending on the system state is being minimized. The finite-time convergence to a vicinity of order e of the optimal equilibrium point is proved.