Module Number: EI7435
Duration: 1 Semester
Occurence: Winter Semester
Number of ECTS: 6
Professor in charge: Wolfgang Utschick
Self-study hours: 120
Written examination (evaluation of basic theoretical concepts presented in the lecture and tutorials). Up to 20% of the examination can be conducted in the form of multiple choice questions.
Exam type: written
Exam duration (min.): 90
Possibility of retaking: In the next semester: Yes. At the end of the semester: No
Written paper: No
Basic Classes in Linear Algebra and Calculus.
Introduction: - basic definitions and fundamentals- problem statement Convex analysis: - convex sets - convex functionsLinear programming: - extremal points and directions - simplex algorithm Optimality conditions: - Fritz John conditions - Karush-Kuhn-Tucker conditions - constraint qualifications Lagrangian duality: - duality theorems Algorithms:- general concept - unconstrained optimization- constrained optimization Solutions for the dual problem: - subgradient method- cutting plane algorithm Interior-point method: - barrier functions - IP algorithmApplications: - problems from multiuser information theory - resource allocation - parameter optimization in layered and distributed communication systems
At the end of the module, students are able to remember, understand and apply the theory, the basic methodologies and algorithms of convex optimization theory, and students are able to analyse and evaluate technical systems from the perspective of optimization theory and are able to create mathematical concepts and numerical algorithms for the optimal design and operation of information and communications systems.
- Learning method: In addition to the individual methods of the students, consolidated knowledge is aspired by repeated lessons in exercises and tutorials.
- Teaching method: During the lectures, the students are instructed in a teacher-centered style. The exercises are held in a student-centered way.
The following kinds of media are used:
- Lecture notes
- Exercises with solutions as download
The following literature is recommended:
- M. S. Bazaara, H. D. Sherali and C. M. Shetty. Nonlinear Programming: Theory and Algorithms. Wiley, 2006
- D. Bertsekas and A. Nedic. Convex Analysis and Optimization. Athena Scientific, 2003
- S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge, 2004