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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 finite-dimensional 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, quasi-Newton methods, conjugate gradients, least-squares 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 Analysis, basic course, or similar knowledge.

Literature

[1] P. E. Gill and M. H. Wright, Numerical nonlinear optimization. Lecture notes.
The course will be based on the lecture notes [1], which is a manuscript.

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 lecture notes will be sold at Elevexpeditionen at the Department of Mathematics, Lindstedtsvägen 25. They cost 100 kronor. The textbooks are not required for the course, and will not be distributed through KTH.

Schedule

Lectures are given Tuesdays 8.15-10.00, in Room 3721, Lindstedtsvägen 25. There will tentatively be 12 lectures.

Examination

The examination is by homework assignments and a final oral exam.

Examiner

Anders Forsgren, room 3703, Lindstedtsvägen 25, tel. 790 71 27. E-mail: andersf@kth.se.

Optimization and Systems Theory, KTH
Anders Forsgren, andersf@kth.se