Optimization Techniques 2025

The course provides an overview of optimization tools and techniques, motivated by large-scale problems that arise in Data Science, and real-life optimisation problems from industrial environments such as transportation, logistics and manufacturing. Optimization is at the heart of various critical tasks related to handling big data and enhancing decision making and a great number of methodologies have been developed over the years. The course aims to make students acquainted with modeling problems as optimization tasks and solving them using a range of exact and near-optimal solution methods.

In the first part, we will study fundamental mathematical modeling techniques, including linear and convex programming, and analyze key solution algorithms such as the simplex method, interior point method, and gradient descent. We will also explore their applications in core machine learning problems (e.g., regression, classification).

In the second part, we will extend our focus to the mathematical modeling of practical combinatorial optimization problems and examine their solutions using: a) exact methods, including branch and bound, decomposition methods, and constraint programming, and b) (meta-)heuristics, such as simulated annealing, genetic algorithms, as well as heuristic approaches that integrate combinatorial optimization with machine learning techniques, such as reinforcement learning (RL). The presentation of these methods will be accompanied by representative case studies demonstrating their application in real-world industrial problems.