A gradient optimization methodology for use with nonlinear envelope simulation is presented. Emphasis is placed on efficient evaluation of cost function gradients. To this end, an envelope sensitivity equation is derived and methods for its efficient solution are proposed. In the case of circuits of moderate size, the solution of the sensitivity equation is shown to be simple and inexpensive. The more troublesome case of larger circuits is treated by a novel application of a recently developed iterative linear equation solver. The result is a general-purpose, rigorous optimization methodology for the fine tuning of gain, adjacent channel power, power efficiency, and related performance measures in radio frequency (RF) amplifiers for digital communications. As an illustrative example, the optimization of a feedforward-linearized power amplifier is presented.