Contents |
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Course Title
Numerical Optimization
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Course Code
IAM 566
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Credit
(3-0)3
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Prerequisites
Consent of the instructors
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Content
Coursework and computer lab with MATLAB.
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Aims
The objective of this course is to introduce the central ideas behind algorithms for the numerical solution of differentiable optimization problems by presenting key methods for both unconstrained and constrained optimization, as well as providing theoretical justification as to why they succeed.
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Learning Outcomes
At the end of this course students should be able to tackle optimization problems of in science, engineering and finance using state of art numerical methods. Both lectures and exercises serve for this aim of learning, deepening, applying and preparing.
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Suggested Textbooks
- G. Nash and Ariela Sofer, Linear and nonlinear programming, New York : McGraw-Hill, 1996, T57.74 N37
- J. Nocedal, S.J. Wright, Numerical Optimization, Springer, 1999, QA 402.5 N62
- S. Ulbrich, M. Ulbrich, “Nonlinear Optimization”, Lecture Notes, Department of Mathematics, University of Technology Darmstadt,
- Lecture Notes are prepared by B. Karasözen and G.-W. Weber and available from IAM Lecture Notes Series.
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Outline
- 1.week: Fundamentals of unconstrained optimization
- 2.week: Newton methods
- 3.week: Line search methods
- 4.week: Trust region methods
- 5.week: Quasi-Newton methods
- 6.week: Nonlinear least squares problems
- 7.week: Theory of constrained optimization
- 8.week: Theory of linear programming
- 9.week: Simplex method
- 10.week: Interior point methods
- 11.week: Interior point methods
- 12.week: Penalty and barrier methods
- 13.week: Sequential Quadratic Programming
- 14.week: Conclusion and outlook on unconstrained and constrained optimization
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Resources
MATLAB 6.1
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First Meeting in Fall 2008-2009
Friday, September 19, 9.40h - 12.30h, in IAM, S 209.