Block Lecture: Computational Integer Optimization (24.08 - 28.08)

Integer optimization lies at the core of many real-world decision problems in logistics, finance, energy systems, and production planning. Solving large-scale mixed-integer programs efficiently requires sophisticated algorithms, numerical rigor, and a deep understanding of the mathematics behind the applications.

This block course focuses on the computational and mathematical foundations of modern integer optimization solvers. In dedicated lectures, we study the algorithmic building blocks that make state-of-the-art solvers effective in practice, as well as the mathematical principles underlying their correctness and performance.

Topics include different classes of cutting planes and techniques to prove their correctness; the mathematical foundations of presolving (with excursions to number theory and graph theory); primal heuristics for finding high-quality feasible solutions; logical deduction mechanisms in propagation and infeasibility analysis; and the integration of machine learning techniques into optimization algorithms. Further emphasis is placed on numerics in limited-precision algebra, software engineering aspects, principled evaluation of algorithms, and best modeling practices in mathematical optimization.

In addition to the lectures, there will be hands-on implementation sessions, working with state-of-the-art optimization software.

Exams are based on lecture content so active participation is highly recommended. Additional materials are given for optional further reading.