Nonconvex Optimization: Challenges and Strategies

This lecture delves into nonconvex optimization problems with nonlinear constraints, focusing on blind image deconvolution as an illustrative example. It covers standard convex optimization formulations, SDP relaxations, and applications in graph theory, clustering, and neural networks. The instructor discusses the challenges in convergence guarantees and introduces strategies like the Homotopy Conditional Gradient Method and Augmented Lagrangian approach.