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

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(h
²
), which is at the same level as those reported in the literature. We demonstrate the validity of the proposed algorithm by a numerical example.