Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-50-12-M-4

Nonlinear Optimization (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-50-12-M-4 Nonlinear Optimization 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. in SuSe
Level [4] Bachelor (Specialization)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-OPT] Optimisation
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Notice

Without a proof of successful participation in the exercise classes, only 6 credit points will be awarded for the module.

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-50-12-K-4
Nonlinear Optimization
P 84 h 186 h
U-Schein
- PL1 9.0 SuSe
  • About [MAT-50-12-K-4]: Title: "Nonlinear Optimization"; Presence-Time: 84 h; Self-Study: 186 h
  • About [MAT-50-12-K-4]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 84320 ("Nonlinear Optimization")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

  • Optimality conditions for unconstraint and constraint optimization problems,
  • One-dimensional minimization; direct search methods,
  • Descent methods in higher dimensions,
  • CG method,
  • Trust region algorithms,
  • Penalty methods,
  • Extended Lagrangian,
  • SQP method,
  • Barrier methods and primal-dual procedures.

Competencies / intended learning achievements

Upon successful completion of the module, the students have studied and understand different methods and algorithms to solve nonlinear optimization problems. They have learnt to model and solve real problems in the areas of economics, engineering and physics by means of transforming them into nonlinear optimization problems using mathematical methods. They are able to critically assess the possibilities and limitations of the use of these methods. They understand the proofs presented in the lecture and are able to comprehend and explain them.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies.

Literature

  • R. Fletcher: Practical methods of optimization,
  • D.G. Luenberger: Linear and Nonlinear Programming,
  • J. Stoer, C. Witzgall: Convexity and Optimization in Finite Dimensions,
  • M.S. Bazaraa, H.D. Sherali, C.M. Shetty: Nonlinear Programming: Theory and Algorithms,
  • K.H. Borgwardt: Optimierung, Operations Research, Spieltheorie: Mathematische Grundlagen,
  • R. Horst, P.M. Pardalos, M.V. Thoai: Introduction to Global Optimization,
  • H. Tuy: Convex Analysis and Global Optimization.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-50-12-M-4]

Course of Study Section Choice/Obligation
[INF-88.79-SG] M.Sc. Computer Science Formal Fundamentals [WP] Compulsory Elective
[MAT-88.B84-SG] M.Sc. Actuarial and Financial Mathematics Statistics and Computational Methods [WP] Compulsory Elective
[MAT-88.105-SG] M.Sc. Mathematics Applied Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International Applied Mathematics [WP] Compulsory Elective
[MAT-88.118-SG] M.Sc. Industrial Mathematics General Mathematics [WP] Compulsory Elective
[MAT-88.276-SG] M.Sc. Business Mathematics General Mathematics [WP] Compulsory Elective