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, SS18)
Präsenzzeiten: 4V 2Ü
ECTS: 9
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

Kurzfassung:

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

Lernziele:

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.

Lehrinhalte:

  • 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

Voraussetzungen:

  • 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.

Prüfungsleistung:

Oral exam

Lehr- und Lernmethoden:

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

Verwendbarkeit:

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.

Literatur:

  • D.G. Luenberger, Y. Ye. Linear and nonlinear programming. 4th ed. Springer 2016.
  • J. Nocedal, S.J. Wright. Numerical optimization. 2nd ed. Springer 2006.
  • P.E. Gill, W. Murray, M.H. Wright: Practical Optimization Academic Press 2nd ed. 1988.
  • Walter Alt. Nichtlineare Optimierung. Eine Einführung in Theorie, Ver- fahren und Anwendungen. Vieweg, August 2002.
  • A. R. Conn, N. I. M. Gould, and P. L. Toint. Trust-region methods. MPS- SIAM series on optimization. Society for Industrial and Applied Mathematics, Philadelphia, 2000.
  • J.E. Dennis and R.B. Schnabel. Numerical methods for unconstrained optimization and nonlinear equations. Society for Industrial Mathematics, 1996.
  • P. Spellucci. Numerische Verfahren der nichtlinearen Optimierung. Birkhäuser, Basel, 1993.
  • J. Werner. Numerische Mathematik 2. Vieweg Studium, Aufbaukurs Mathematik. Vieweg, 1992.
  • Edwin K. P. Chong; Stanislaw H. Zak: An introduction to optimization, John Wiley & Sons 2013.

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