KTH /
Engineering Science
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Mathematics
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Optimization and Systems Theory
SF3840 Numerical nonlinear programming, 7.5cr
General information
This course is primarily intended for graduate students in optimization
and systems theory, or other graduate students with a good background in
optimization.
Summary of contents
The course deals with algorithms and fundamental theory for nonlinear
finitedimensional optimization problems. Fundamental optimization
concepts, such as convexity and duality are also introduced. The main
focus is nonlinear programming, unconstrained and constrained. Areas
considered are unconstrained minimization, linearly constrained
minimization and nonlinearly constrained minization. The focus is on
methods which are considered modern and efficient today.
Unconstrained nonlinear programming: optimality conditions, Newton
methods, quasiNewton methods, conjugate gradients, leastsquares
problems.
Constrained nonlinear programming: optimality conditions, quadratic
programming, SQP methods, penalty methods, barrier methods, dual
methods.
Linear programming is treated as a special case of nonlinear
programming.
Semidefinite programming and linear matrix inequalities are also
covered.
Prerequisites
Suitable prerequisites are the courses SF2822 Applied Nonlinear
Optimization, DN2251 Applied Numerical Methods III and SF2713
Foundations of Analysis, or similar knowledge.
Literature
[1] 
P. E. Gill and M. H. Wright,
Computational optimization: Nonlinear programming.
Lecture notes.

The lecture notes [1] are available
at Bilda
in the form of a pdf file.
Students may, if they wish, choose textbooks such as [2], [3] and [4] for
supplementary reading.
[2] 
P. E. Gill, W. Murray, and M. H. Wright.
Practical Optimization,
Academic Press, London and New York, 1981. 
[3] 
D. Bertsekas.
Nonlinear Programming,
Athena Scientific, 1996. 
[4] 
J. Nocedal and S. J. Wright.
Numerical Optimization,
Springer, 1999.

The textbooks are not required for the course, and will not be
distributed through KTH.
Schedule
Lectures are held Wednesdays 13.1515.00 in Room
3733, Lindstedtsvägen 25.
There will tentatively be 12 lectures, one lecture a week.
Examination
The examination is by five sets of homework assignments and a final oral exam.
Examiner
Anders Forsgren, room 3533,
Lindstedtsvägen 25, tel. 790 71 27. Email: andersf@kth.se.
