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Same material as EN.601.481, for graduate students. Optimization is at the heart of machine learning. Most machine learning problems can be posed as optimization problems. However, unlike mathematical optimization where the focus is on efficient algorithms for finding solutions with a high degree of accuracy as measured by optimality conditions, optimization for machine learning focuses on algorithms that are efficient and generalize well. In this course, we will focus on optimization for problems that arise in machine learning, design and analysis of algorithms for solving these problems, and the interplay of optimization and machine learning. The coursework will include homework assignments and a final project focusing on applying optimization algorithms to real world machine learning problems. [Analysis or Applications] Required Course Background: EN 601.475/675 Machine Learning or all of the following: 1. Linear algebra (vector spaces, normed vectors, inner product spaces, singular value decomposition 2. Probability and Statistics (random variables, probability distributions, expectation, mean, variance, covariance, conditional probability, Bayes rule 3. Introductory machine learning (classification, regression, empirical risk minimization, regularization) 4. Multivariate calculus (partial derivative, gradient, Jacobian, Hessian, critical points