Principles and applications of convex optimization in data science, econometrics and machine learning.

This course delves into the principles and applications of convex optimization, with a particular emphasis on its role in data science, econometrics and machine learning. Students explore fundamental theories and algorithms in convex optimization, gaining insights into how these techniques are used to solve complex problems, such as training machine learning models, estimating large-scale econometric models, and optimal investment problems.

Through practical examples and exercises, students learn to formulate and solve optimization problems, understand the convergence properties of various algorithms, and apply these methods to real-world examples. Students learn to analyse problems rigorously through convexity, duality and optimality conditions, and then discover how modern solvers, based on interior-point methods and barrier functions, work under the hood to solve large-scale optimization problems efficiently.

Stephen Boyd and Lieven Vandenberghe (2004), Convex Optimization, Cambridge University Press. ISBN: 978-0-521-83378-3

Students should have knowledge of linear algebra, basic probability theory, matrix/vector calculus. Also note that Python programming skills are required for all the cases, as these involve numerical calculations using the package CVXPY.