This paper presents an augmented optimal power flow (OPF) formulation that minimizes a power network's transient control costs using a linear quadratic regulator (LQR). The network is described by AC power flows with third-order generator dynamics modeling. Then, linearized dynamics around a known solution of the power flow equations are considered. Leveraging the equivalent linear matrix inequality formulation for the LQR, the augmented OPF (LQR-OPF) amounts to a semidefinite program, yielding optimal network steady state and an explicit feedback gain for minimum transient control cost. Numerical tests on a standard power network demonstrate the advantage of LQR-OPF in comparison to a scheme where OPF and transient control are solved separately.