University of Delaware 3 credits ELEG
Optimization algorithms form a foundation for numerous modern methods in signal processing, machine learning, and data science. This course provides an introduction to powerful techniques and fundamental theory for optimization in these contexts. The goal is for students to become fluent in using modern optimization techniques (through hands-on experience computing numerical solutions to challenging optimization problems in signal processing, machine learning, and data science) and to learn how to use these tools wisely (by understanding the underlying theory and trade-offs). Potential topics include: First order methods and theory for smooth optimization (gradient methods, accelerated gradient methods, stochastic gradient methods) Second order methods and theory for smooth optimization (Newton and quasi-Newton methods) Non-smooth optimization methods and theory (subgradient methods, proximal methods) Constrained optimization methods and theory (projected gradient methods, interior point methods, ADMM, manifold optimization methods) Optimization transfer methods (expectation maximization, majorize-minimize, mirror descent) Convexity, duality, and optimality conditions Taxonomy of optimization problems (including linear, quadratic, and semidefinite programs) Restrictions: Knowledge on linear algebra, vector calculus, and probability recommended.
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