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Event

Nonlinear Optimization I [WS222550111]

Type
lecture (V)
Präsenz
Term
WS 22/23
SWS
2
Language
Deutsch
Appointments
29
Links
ILIAS

Lecturers

Organisation

  • Kontinuierliche Optimierung

Part of

Literature

O. Stein, Grundzüge der Nichtlinearen Optimierung, 2. Aufl., SpringerSpektrum, 2021

Weiterführende Literatur:

  • W. Alt, Nichtlineare Optimierung, Vieweg, 2002
  • M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming, Wiley, 1993
  • O. Güler, Foundations of Optimization, Springer, 2010
  • H.Th. Jongen, K. Meer, E. Triesch, Optimization Theory, Kluwer, 2004
  • J. Nocedal, S. Wright, Numerical Optimization, Springer, 2000

Appointments

  • 26.10.2022 09:45 - 11:15 - Room: 10.11 Seminarraum Hauptgebäude
  • 28.10.2022 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
  • 02.11.2022 09:45 - 11:15 - Room: 10.11 Seminarraum Hauptgebäude
  • 04.11.2022 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
  • 11.11.2022 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
  • 16.11.2022 09:45 - 11:15 - Room: 10.11 Seminarraum Hauptgebäude
  • 18.11.2022 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
  • 23.11.2022 09:45 - 11:15 - Room: 10.11 Seminarraum Hauptgebäude
  • 25.11.2022 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
  • 30.11.2022 09:45 - 11:15 - Room: 10.11 Seminarraum Hauptgebäude
  • 02.12.2022 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
  • 07.12.2022 09:45 - 11:15 - Room: 10.11 Seminarraum Hauptgebäude
  • 09.12.2022 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
  • 14.12.2022 09:45 - 11:15 - Room: 10.11 Seminarraum Hauptgebäude
  • 16.12.2022 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
  • 21.12.2022 09:45 - 11:15 - Room: 10.11 Seminarraum Hauptgebäude
  • 23.12.2022 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
  • 11.01.2023 09:45 - 11:15 - Room: 10.11 Seminarraum Hauptgebäude
  • 13.01.2023 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
  • 18.01.2023 09:45 - 11:15 - Room: 10.11 Seminarraum Hauptgebäude
  • 20.01.2023 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
  • 25.01.2023 09:45 - 11:15 - Room: 10.11 Seminarraum Hauptgebäude
  • 27.01.2023 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
  • 01.02.2023 09:45 - 11:15 - Room: 10.11 Seminarraum Hauptgebäude
  • 03.02.2023 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
  • 08.02.2023 09:45 - 11:15 - Room: 10.11 Seminarraum Hauptgebäude
  • 10.02.2023 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
  • 15.02.2023 09:45 - 11:15 - Room: 10.11 Seminarraum Hauptgebäude
  • 17.02.2023 09:45 - 11:15 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)

Note

The lecture treats the minimization of smooth nonlinear functions without constraints. For such problems, which occur very often in economics, engineering, and natural sciences, optimality conditions are derived and, based on them, solution algorithms are developed. The lecture is structured as follows:

  • Introduction, examples, and terminology
  • Existence results for optimal points
  • First and second order optimality condtions
  • Algorithms (line search, steepest descent method, variable metric methods, Newton method, Quasi Newton methods, CG method, trust region method)

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 optimization problems with constraints forms the contents of the lecture "Nonlinear Optimization II". The lectures "Nonlinear Optimization I" and "Nonlinear Optimization II" are held consecutively in the same semester.

Learning objectives:

The student

  • knows and understands fundamentals of unconstrained nonlinear optimization,
  • is able to choose, design and apply modern techniques of unconstrained nonlinear optimization in practice.