Event
Nonlinear Optimization I [WS212550111]
Lecturers
Organisation
- Kontinuierliche Optimierung
Part of
- Brick Nonlinear Optimization I | Industrial Engineering and Management (M.Sc.)
- Brick Nonlinear Optimization I | Industrial Engineering and Management (B.Sc.)
- Brick Nonlinear Optimization I and II | Industrial Engineering and Management (M.Sc.)
- Brick Nonlinear Optimization I and II | Industrial Engineering and Management (B.Sc.)
- Brick Nonlinear Optimization I | Economics Engineering (M.Sc.)
- Brick Nonlinear Optimization I | Economics Engineering (B.Sc.)
- Brick Nonlinear Optimization I and II | Economics Engineering (M.Sc.)
- Brick Nonlinear Optimization I and II | Economics Engineering (B.Sc.)
- Brick Nonlinear Optimization I | Information Systems (M.Sc.)
- Brick Nonlinear Optimization I | Information Systems (B.Sc.)
- Brick Nonlinear Optimization I and II | Information Systems (M.Sc.)
- Brick Nonlinear Optimization I and II | Information Systems (B.Sc.)
- Brick Nonlinear Optimization I | Information Engineering and Management (B.Sc.)
- Brick Nonlinear Optimization I | Information Engineering and Management (M.Sc.)
- Brick Nonlinear Optimization I and II | Information Engineering and Management (B.Sc.)
- Brick Nonlinear Optimization I and II | Information Engineering and Management (M.Sc.)
- Brick Nonlinear Optimization I | Economathematics (M.Sc.)
- Brick Nonlinear Optimization I and II | Economathematics (M.Sc.)
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
- 20.10.2021 12:00 - 13:30 - Room: 10.11 Seminarraum Hauptgebäude
- 22.10.2021 10:00 - 11:30 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
- 27.10.2021 12:00 - 13:30 - Room: 10.11 Seminarraum Hauptgebäude
- 29.10.2021 10:00 - 11:30 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
- 03.11.2021 12:00 - 13:30 - Room: 10.11 Seminarraum Hauptgebäude
- 05.11.2021 10:00 - 11:30 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
- 10.11.2021 12:00 - 13:30 - Room: 10.11 Seminarraum Hauptgebäude
- 12.11.2021 10:00 - 11:30 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
- 19.11.2021 10:00 - 11:30 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
- 26.11.2021 10:00 - 11:30 - Room: 30.35 Hochspannungstechnik-Hörsaal (HSI)
- 01.12.2021 12:00 - 13:30 - Room: 10.11 Seminarraum Hauptgebäude
- 03.12.2021 10:00 - 11:30 - 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.