This course introduces the fundamentals of convex optimization, with a particular focus on algorithmic aspects and applications in economics and data science. By the end of the course, students will be able to:
•formulate decision problems in machine learning and statistics as mathematical optimization models;
•develop a solid understanding of convex optimization problems;
•implement scalable and accurate versions of the most important optimization algorithms used in economics,
•machine learning, and data science;
•analyze trade-offs between accuracy and computational cost in optimization methods;
•evaluate the performance of algorithms, relevant function classes, and convergence guarantees.
The course provides an overview of modern optimization methods with a focus on applications in economics, machine learning, and data science. Special attention will be given to the scalability of algorithms to large datasets, both in theory and implementation.
Preliminary course structure:
1.Convex optimization
•Optimization problems
•Convex sets, convex functions, convex optimization problems
•Lagrangian duality
•Optimality conditions
•Applications in econometrics, statistics, and machine learning
2.Algorithms
•Gradient descent
•Projected gradient descent
•Stochastic gradient descent
•Newton methods.
