Explore nonconvex optimization techniques in matrix optimization and distributionally robust optimization through this 55-minute lecture by Stephen Wright from the University of Wisconsin. Delivered at the Intersections between Control, Learning and Optimization 2020 conference, hosted by the Institute for Pure and Applied Mathematics at UCLA. Delve into topics such as unconstrained nonconvex complexity, algorithms for smooth nonconvex optimization, operation complexity, line search Newton CG procedures, and nonconvex optimization in machine learning. Examine computational results, the matrix completion problem, and learn about smoothing the ramp loss function. Gain insights into the motivations, context, and practical applications of these advanced optimization techniques in various fields.