This graduate-level course introduces optimization methods that are suitable for large-scale problems arising in data science and machine learning applications. We will first explore several algorithms that are efficient for both smooth and nonsmooth problems, including gradient methods, proximal methods, mirror descent, Nesterov's accelerated methods, ADMM, quasi-Newton methods, stochastic optimization, variance reduction, as well as distributed optimization. We will then discuss the efficacy of these methods in concrete data science problems, under appropriate statistical models. Finally, we will introduce a global geometric analysis to characterize the nonconvex landscape of the empirical risks in several high-dimensional estimation and learning problems.
9/27: Homework 1 is out (see Blackboard). It is due on Wednesday, Oct. 9
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