Technische Universität Ilmenau

Systems Optimization - Modultafeln of TU Ilmenau

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module properties Systems Optimization in degree program Master Communications and Signal Processing 2021
module number200008
examination number2200638
departmentDepartment of Computer Science and Automation
ID of group 2212 (Simulation and Optimal Processes)
module leaderProf. Dr. Pu Li
term winter term only
credit points5
on-campus program (h)45
self-study (h)105
obligationelective module
examwritten examination performance, 90 minutes
details of the certificate
signup details for alternative examinations
maximum number of participants
previous knowledge and experience

Fundamentals of Mathematics and Control Engineering

learning outcome


The students know and can explain

  • fundamentals, problem formulation, and classification of optimization methods
  • methods and tools for optimization
  • different problem formulations and mathematical derivation of optimization methods
  • applications in industrial processes
The students have learned the theory, models, methods, and algorithms of the corresponding subjects in the lectures. In the exercises, they had been activated to solve example tasks.


Linear Optimization:

Theory of linear programming, degree of freedom, feasible region, graphical description/solution, Simplex method, mixing problem, optimal production planning

Nonlinear Optimization:
Convexity analysis, problems without uand with constraints, optimality condition, the gradient-, Newton-, Quasi-Newton-methods, KKT conditions, sequential quadratic programming (SQP) methods, active-set method, approximation of the Hessian matrix, application in optimal design of industrial processes.

Mixed-Integer Optimization :
Mixed-Integer Linear Programming (MILP), Branch-and-Bound method, optimization software GAMS, application in optimal design of industrial processes.

Dynamic Optimization:

Discretization in time, Euler method, orthogonal collocation, solution of the problem with SQP

media of instruction

Presentation, lecture slides script, blackboard presentation

literature / references


U. Hoffmann, H. Hofmann: Einführung in die Optimierung, Verlag Chemie, Weinheim, 1982

T. F. Edgar, D. M. Himmelblau: Optimization of Chemical Processes, McGraw-Hill, New York, 1989

Teo, K. L., Goh, C. J., Wong, K. H: A Unified Computational Approach to Optimal Control Problems. John Wiley & Sons, New York, 1991

C. A. Floudas: Nonlinear and Mixed-Integer Optimization, Oxford University Press, 1995

L. T. Biegler, I. E. Grossmann, A. W. Westerberg: Systematic Methods of Chemical Process Design. Prentice Hall, New Jersey, 1997

M. Papageorgiou: Optimierung, Oldenbourg Verlag, München, 2006

J. Nocedal, S. J. Wright: Numerical Optimization, Springer-Verlag, 1999

evaluation of teaching