# FSF3840 Numerical Nonlinear Programming 7.5 credits

This course is primarily intended for graduate students in optimization and systems theory, or other graduate students with a good background in optimization.

### Choose semester and course offering

Choose semester and course offering to see current information and more about the course, such as course syllabus, study period, and application information.

Headings with content from the Course syllabus FSF3840 (Spring 2019–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course 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.

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

Semidefinite programming and linear matrix inequalities are also covered.

### Intended learning outcomes

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

Lectures.

## Literature and preparations

### Specific prerequisites

A Master degree including at least 30 university credits (hp) in in Mathematics (Calculus, Linear algebra, Differential equations and transform method), and further at least  6 hp in Mathematical Statistics, 6 hp in Numerical analysis and 6 hp in Optimization.

### Recommended prerequisites

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

### Equipment

No information inserted

### Literature

Announced when the course is offered.

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

P, F

### Examination

• 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.

### Other requirements for final grade

Homework assignments and a final oral exam.

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### Ethical approach

• 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.

## Further information

### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web FSF3840

### Main field of study

This course does not belong to any Main field of study.

Third cycle