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.

Linear programming is treated as a special case of nonlinear programming.

Semidefinite programming and linear matrix inequalities are also covered.

That the student should obtain a deep understanding of the mathematical theory and the numerical methods for nonlinear programming.

After completed course, the student should be able to

• Derive optimality conditions for different classes of nonlinear optimization problems.

• Explain how the method of steepest descent, the method of conjugate gradients, quasi-Newton methods and Newton methods work for unconstrained optimization, both linesearch methods and trust-region methods

• Explain methods related to the above for equality-constrained problems

• Explain methods related to the above for inequality-constrained problems

• Explain how interior methods for semidefinite programming work

The course consists of 24h lectures, given during periods 1 and 2, autumn 2021.

Lectures will be given in Room 3418, Lindstedtsvägen 25.

There will be five sets of homeworks and an oral final exam. Homework assignment and other material related to the course will be posted in Canvas.

Suitable prerequisites are the courses SF2822 Applied Nonlinear Optimization, SF2520 Applied Numerical Methods and SF2713 Foundations of Analysis, or similar knowledge.

1. P. E. Gill and M. H. Wright, Computational optimization: Nonlinear programming. Lecture notes.

The lecture notes [1] will be made available in Canvas in the form of a pdf file.

Students may, if they wish, choose textbooks such as [a], [b] and [c] for supplementary reading.

1. P. E. Gill, W. Murray, and M. H. Wright. Practical Optimization, Academic Press, London and New York, 1981.
2. D. Bertsekas. Nonlinear Programming, Athena Scientific, 1996.
3. 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.

Students at KTH with a permanent disability can get support during studies from Funka:

Funka - compensatory support for students with disabilities

P, F

• INL1 - Assignment, 7.5 credits, Grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

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

Assignment ( INL1 )

Homework assignments and a final oral exam.

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.