Running Primal-Dual Gradient Method for Time-Varying Nonconvex Problems

This paper focuses on a time-varying constrained nonconvex optimization problem, and considers the synthesis analysis of online regularized primal-dual gradient methods to track Karush--Kuhn--Tucker (KKT) trajectory. The proposed method is implemented in running fashion, sense that underlying problem changes during execution algorithms. In order study its performance, we first derive continuous-time limit as system differential inclusions. We then sufficient conditions for tracking KKT trajectory, also asymptotic bounds error (as function time-variability trajectory). Further, provide set trajectories not bifurcate or merge, investigate optimal choice parameters algorithm. Illustrative numerical results are provided.