  Time-varying optimization problems are prevalent in various engineering
fields, and the ability to solve them accurately in real-time is becoming
increasingly important. The prediction-correction algorithms used in smooth
time-varying optimization can achieve better accuracy than that of the
time-varying gradient descent (TVGD) algorithm. However, none of the existing
prediction-correction algorithms can be applied to general non-strongly-convex
functions, and most of them are not computationally efficient enough to solve
large-scale problems. Here, we propose a new prediction-correction algorithm
that is applicable to large-scale and general non-convex problems and that is
more accurate than TVGD. Furthermore, we present convergence analyses of the
TVGD and proposed prediction-correction algorithms for non-strongly-convex
functions for the first time. In numerical experiments using synthetic and real
datasets, the proposed algorithm is shown to be able to reduce the convergence
error as the theoretical analyses suggest and outperform the existing
algorithms.
