Many problems in machine learning today can be cast as minimizing a convex loss function subject to some inequality constraints. As a result, the success of machine learning today depends on convex optimization methods that can scale to sizes reaching that of the World Wide Web. Problems in this class include basis pursuit, compressed sensing, graph reconstruction via precision matrix estimation, matrix completion under rank constraints, etc. One of the most popular optimization methods to use is the Alternating Direction Method of Multipliers. This is extremely well-scalable, but the convergence rate can be erratic. In this talk I will introduce the problem and algorithm with some applications and show how linear algebra can explain the erratic behavior. [Go to the full record in the library's catalogue]
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