Convex Optimization for Statistics and Data Science

Catalog description

Convex optimization has become a real pillar of modern data science and has transformed algorithm designs. A wide spectrum of problems in statistics, machine learning, and engineering can be formulated as optimization tasks that exhibit favorable convexity properties, which admit standardized and efficient solutions. This course aims to introduce the elements of convex optimization, concentrating on modeling aspects and algorithms that are useful in data science applications. Topics include convex sets, convex functions, linear and quadratic programs, semidefinite programming, optimality conditions and duality theory. We will visit important applications in statistics and machine learning to demonstrate the wide applicability of convex optimization. We will also cover effective optimization algorithms like gradient descent and Newton's method. Prerequisites: Basic linear algebra (Math 3120, 3130, 3140 or equivalent), basic calculus (Math 2400 or equivalent), basic probability ( STAT 4300 or equivalent), and knowledge of a programming language like MATLAB or Python to conduct simulation exercises.