A Second-Order Saddle Point Method for Time-Varying Optimization

Time-varying optimization studies algorithms that can track solutions of optimization problems that evolve with time. A typical time-varying optimization algorithm is implemented in a running fashion in the sense that the underlying optimization problem is updated during the iterations of the algorithm, and is especially suitable for optimizing large-scale fast varying systems. In this paper, we propose and analyze a second-order method for time-varying optimization. Each iteration of the proposed method can be formulated as solving a quadratic-like saddle point problem that incorporates curvature information. Theoretical results on the tracking performance of the proposed method are presented, and discussions on their implications and comparison with existing second-order and first-order methods are also provided.