Nichtlineare Optimierung Show URL Convert to PDF XML representation


Modulcode: Inf-NLinOpt
Englische Bezeichnung: Nonlinear Optimization
Modulverantwortliche(r): Prof. Dr. Thomas Slawig
Turnus: unregelmäßig (SS17)
Präsenzzeiten: 4V 2Ü
Workload: 270 Std.
Dauer: ein Semester
Modulkategorien: IG (MSc Inf.) TG (MSc Inf.) MV (MSc Inf.) MSc Math (Export) WI (MSc WInf. (15)) WI (MSc Inf (15)) WI (MEd Inf) WPI (MEd Inf)
Lehrsprache: Englisch


Theory and numerical methods for nonlinear optimization problems for real variables without and with constraints are discussed.


The students know the fundamental theoretical results for nonlinear constrained and unconstrained optimization problems in real variables. They are able to analyze problems, to select and implement algorithms. They are able to present results, analyze them and draw conclusions w.r.t. performance and quality improvement. An additional focus is on theoretical aspects of numerical optimization methods, e.g. the proofs of important theorems or results.


  • Problem statement and classification
  • Existence and uniqueness results
  • Optimality conditions of first and second order
  • Convex problems
  • General descent methods
  • Gradient and conjugate gradient methods
  • Newton and Quasi-Newton methods
  • Trust region methods
  • Derivative-free methods
  • Lagrange multiplier rules
  • Penalty and barrier methods
  • Lagrange methods


  • Mathematics: linear algebra (linear systems, eigenvalues and eigenvectors of symmetric matrices), multi-dimensional calculus and Taylor expansion
  • Programming in a higher language or Matlab/Octave/Python.


Oral or written exam based on implementation performed during the course exercises.

Lehr- und Lernmethoden:

Lectures, group exercises, discussions, self-study and computer work in groups.


MSc Computer Science, MSc Mathematics, MSc Computational Science and Engineering, area Optimization and Optimal Control. Cannot be used as Nebenfach Computer Science in MSc Mathematics.


  • Nocedal Wright: Nonlinear optimization, Wiley
  • Luenberger: Linear and Nonlinear Programming, Springer
  • Edwin K. P. Chong; Stanislaw H. Zak: An introduction to optimization, Wiley 2013