A simplified prediction-correction algorithm for time-varying convex optimization

Abstract

This paper studies a time-varying unconstrained convex optimization problem under the prediction-correction scheme. Our primary objective is to devise a simplified prediction-correction algorithm, which can solve the time-varying unconstrained convex optimization problem effectively without the need to compute the inverse of the Hessian matrix of the cost function. To this aim, we propose a simplified prediction step and provide the theoretical analysis on the convergence of the resulting algorithm. The results show that, under suitable conditions, the error bound of our algorithm is O(h2), which is at the same level as those reported in the literature. We demonstrate the validity of the proposed algorithm by a numerical example.