2550134 – Global Optimization I

Lecturer: Prof. Dr. Oliver Stein, Institute for Operations Research

Time and place:
Wednesday, 11:30 - 13:00, 11.10 Kl. HS E-Technik, and
Friday, 9:45 - 11:15, 10.91-Redtenbacher.

Start: Wednesday, April 22, 2026.

Format: In-person lecture.

Assessment: Successful participation in mandatory prerequisite (online tests) and a written exam.

Content:
In many optimization problems from economics, engineering and natural sciences, solution algorithms are only able to efficiently identify local optimizers, while it is much harder to find globally optimal points. This corresponds to the fact that by local search it is easy to find the summit of the closest mountain, but that the search for the summit of Mount Everest is rather elaborate.

The lecture treats methods for global optimization of convex functions under convex constraints. It is structured as follows:

• Introduction, examples, and terminology
• Existence results for optimal points
• Optimality in convex optimization
• Duality, bounds, and constraint qualifications
• Algorithms (Kelley's cutting plane method, Frank-Wolfe method, primal-dual interior point methods)

The treatment of nonconvex optimization problems forms the contents of the lecture Global Optimization II.

The lectures Global Optimization I and Global Optimization II are held consecutively within the same semester.

The lecture is accompanied by exercises which, amongst others, offers the opportunity to implement and to test some of the methods on practically relevant examples.

Exercises: (Instructor: Emilia Huber)
Wednesday, 14:00 - 15:30, 11.10 Kl. HS E-Technik
Start: April 22, 2026.

Literature:
W. Alt, Numerische Verfahren der konvexen, nichtglatten Optimierung, Teubner, 2004.
C.A. Floudas, Deterministic Global Optimization, Kluwer, 2000.
R. Horst, H. Tuy, Global Optimization, Springer, 1996.
A. Neumaier, Interval Methods for Systems of Equations, Cambridge University Press, 1990.
O. Stein, Basic Concepts of Global Optimization, Springer, 2024.

Englisch

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Bis: 1. Apr 2027, 00:00

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