Numerical Optimization


Teacher: Alberto Bemporad

Course description

Optimization plays a key role in solving a large variety of decision problems that arise in engineering (design, process operations, embedded systems), data science, machine learning, business analytics, finance, economics, and many others. This course focuses on formulating optimization models and on the most popular numerical methods to solve them.

Syllabus

Modeling: linear programming models, convex optimization models. Basic optimization theory: optimality conditions, sensitivity, duality. Algorithms for constrained convex optimization: active-set methods for linear and quadratic programming, proximal methods and ADMM, stochastic gradient, interior-point methods. Line-search methods for unconstrained nonlinear programming, sequential quadratic programming.

Prerequisites

Linear algebra and matrix computation, calculus and mathematical analysis.

Timetable

Monday December 1, 2026 09:00-11:00, 14:00-18:00
Tuesday December 2, 2026 09:00-11:00, 14:00-18:00
Wednesday December 3, 2026 09:00-11:00, 14:00-18:00
Thursday December 4, 2026 09:00-11:00, 14:00-18:00
Friday December 5, 2026 09:00-11:00, 14:00-18:00

Location

Hybrid mode: IMT School, Piazza San Francesco, 19 - Lucca / Online.

Lecture slides

Optimization models, linear and convex programming (updated 5/12/2024)
Optimization theory (optimality conditions, duality) (updated 6/12/2024)
Basics of numerical linear algebra (updated 11/11/2024)
Active-set methods (updated 11/11/2024)
Operator splitting methods (proximal gradient, ADMM), stochastic gradient descent (updated 11/12/2024)
Unconstrained nonlinear optimization, interior-point methods (updated 14/12/2024)