We present a novel open-loop control method for an electrostatically actuated optofluidic refractive phase modulator, and demonstrate its performance for high-order aberration correction. Contrary to conventional electrostatic deformable mirrors, an optofluidic modulator is capable of bidirectional (push-pull) actuation through hydro-mechanical coupling. Control methods based on matrix pseudo-inversion, the common approach used for deformable mirrors, thus perform sub-optimally for such a device. Instead, we formulate the task of finding driving voltages for a given desired wavefront shape as an optimization problem with inequality constraints that can be solved using an interior-point method in real time. We show that this optimization problem is a convex one and that its solution represents a global minimum in residual wavefront error. We use the new method to control both the refractive phase modulator and a conventional electrostatic deformable mirror, and experimentally demonstrate improved correction fidelity for both.