Theory of Nonconvex Optimization: Phase Retrieval and Beyond

In machine learning and signal processing, due to the nonlinear system or latent low-rank structure of the data, many nonconvex optimization methods have been implemented with remarkable performance. In contrast to convex approaches, nonconvex methods could be more computationally fast, while the theoretical framework would be more difficult due to potential undesirable local minima. In this talk, I will introduce some theoretical frameworks to analyze nonconvex optimization in phase retrieval and other related problems.