We describe an approach to coronagraphic focal-plane wavefront control that utilizes gradient-based nonlinear optimization along with analytical gradients obtained with algorithmic differentiation to find deformable mirror solutions. In addition to eliminating the cost of calculating a high-dimensional finite-difference Jacobian matrix, we show that this approach leads to improved asymptotic computational efficiency. With very high-actuator deformable mirrors such as the 128  ×  128 actuators baselined for the Large UV/Optical/IR Surveyor mission concept, the proposed algorithm reduces memory consumption by approximately 95  %   compared to a Jacobian-based algorithm.