Prediction Correction Interior Point Method for Time Varying Convex Optimization
In this paper, we develop an interior point method for solving a class of convex optimization problems with time varying objective and constraint functions. Using log barrier penalty functions, we propose a continuous time dynamical system for tracking the (time varying) optimal solution with an asymptotically vanishing error. This dynamical system is composed of two terms: a correction term consisting of a continuous time version of Newton's method, and a prediction term able to track the drift of the optimal solution by taking into account the time varying nature of the objective and constraint functions. Using appropriately chosen time varying slack and barrier parameters, we ensure that the solution to this dynamical system globally asymptotically converges to the optimal solution at an exponential rate. We illustrate the applicability of the proposed method in two applications: a sparsity promoting least squares problem and a collision free robot navigation problem.
IEEE Transactions on Automatic Control