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Event

Global Optimization II [SS222550136]

Type
lecture (V)
Präsenz
Term
SS 2022
SWS
2
Language
Deutsch
Appointments
13
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

  • 17.06.2022 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 22.06.2022 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 24.06.2022 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 29.06.2022 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 01.07.2022 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 06.07.2022 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 08.07.2022 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 13.07.2022 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 15.07.2022 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 20.07.2022 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 22.07.2022 09:45 - 11:15 - Room: 10.91 Ferdinand-Redtenbacher-Hörsaal
  • 27.07.2022 11:30 - 13:00 - Room: 30.46 Neuer Hörsaal Chemie
  • 29.07.2022 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 nonconvex functions under nonconvex constraints. It is structured as follows:

  • Introduction and examples
  • Convex relaxation
  • Interval arithmetic
  • Convex relaxation via alphaBB method
  • Branch-and-bound methods
  • Lipschitz optimization

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 convex optimization problems forms the contents of the lecture "Global Optimization I". 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 nonconvex case,
  • is able to choose, design and apply modern techniques of deterministic global optimization in the nonconvex case in practice.