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Event

Global Optimization I [SS232550134]

Type
lecture (V)
Präsenz
Term
SS 2023
SWS
2
Language
Deutsch
Appointments
28
Links
ILIAS

Lecturers

Organisation

  • Kontinuierliche Optimierung

Part of

Literature

O. Stein, Grundzüge der Globalen Optimierung, SpringerSpektrum, 2018.

Weiterführende Literatur:

  • 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

Appointments

  • 19.04.2023 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 21.04.2023 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 26.04.2023 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 28.04.2023 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 03.05.2023 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 05.05.2023 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 10.05.2023 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 12.05.2023 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 17.05.2023 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 19.05.2023 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 24.05.2023 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 26.05.2023 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 07.06.2023 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 09.06.2023 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 14.06.2023 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 16.06.2023 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 21.06.2023 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 23.06.2023 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 28.06.2023 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 30.06.2023 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 05.07.2023 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 07.07.2023 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 12.07.2023 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 14.07.2023 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 19.07.2023 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 21.07.2023 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 26.07.2023 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 28.07.2023 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal

Note

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

Remark:

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 in the same semester.

Learning objectives:

The student

  • knows and understands the fundamentals of deterministic global optimization in the convex case,
  • is able to choose, design and apply modern techniques of deterministic global optimization in the convex case in practice.