Interior point method for dynamic constrained optimization in continuous time

This paper considers a class of convex optimization problems where both the objective function and the constraints have a continuous dependence on time. We develop an interior point method that asymptotically succeeds in tracking the optimal point in nonstationary settings. The method utilizes a time-varying constraint slack and a prediction-correction structure that relies on time derivatives of functions and constraints and Newton steps in the spatial domain. Error free tracking is guaranteed under customary assumptions on the optimization problems and time differentiability of objective and constraints. The effectiveness of the method is illustrated in a target tracking problem.