Abstract

Continuously varying optimization programs have appeared as a natural extension of time-invariant ones when the cost function, the constraints, or both, depend on a time parameter and change continuously in time. This setting captures relevant control, signal processing, and machine learning problems. Recently, running and prediction-correction methods have been put forward to set up iterative algorithms that sample the continuously-varying optimization program at discrete time steps track the optimizer(s) trajectory while it evolves in time up to an asymptotical error bound.In this talk, we will review current state-of-the-art algorithms in time-varying optimization, with a special emphasis on applications in power grids. We will touch upon time-varying AC optimal power flow problems, real-time optimization of aggregations of distributed energy resources, as well as dynamic distribution state estimation.