# SF2822 Applied Nonlinear Optimization 7.5 credits

The course gives deepened and broadened theoretical and methodological knowledge in nonlinear programming. Some subjects dealt with in the course are: Sequential-quadratic-programming methods, primal-dual interior methods, semidefinite programming, convexity, convex relaxations.

The course also gives training in modeling and solving practical problems, and to present the results in talking as well as in writing.

### Choose semester and course offering

Choose semester and course offering to see information from the correct course syllabus and course offering.

Headings with content from the Course syllabus SF2822 (Autumn 2020–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

• Unconstrained optimization: optimality conditions: Newton methods, quasi-Newton methods, conjugate gradient methods.
• Constrained optimization: optimality conditions, quadratic programming, sequential quadratic programming, barrier methods, primal-dual interior methods.
• Semidefinite programming including interior methods.
• Convexity and convex relaxations.

### Intended learning outcomes

To pass the course, the student should be able to do the following:

• Apply theory, concepts and methods from the parts of optimization that are given by the course contents to solve problems.
• Model, formulate and analyze simplified practical problems as optimization problems and solve by making useof given software.
• Collaborate with other students and demonstrate ability to present orally and in writing.

• Combine and explain the methods in the course, and
• Apply and explain the theory and the concepts of the course in the practical problems that are included.

### Course disposition

No information inserted

## Literature and preparations

### Specific prerequisites

• Completed basic coursein optimization (SF1811, SF1861 or equivalent)
• Completed basic course in mathematical statistics (SF1914, SF1918, SF1922 or equivalent)
• Completed basic course in numerical analysis (SF1544, SF1545 or equivalent)
• Completed basic course in differential equations (SF1633, SF1683 or equivalent).

### Recommended prerequisites

A completed continuationcourse in numerical analysis.

### Equipment

No information inserted

### Literature

To be announced at the beginning of the course. Preliminary literature:

Linear and Nonlinear Programming by S.G.Nash och A.Sofer, McGraw-Hill, and some material from the department.

## Examination and completion

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

A, B, C, D, E, FX, F

### Examination

• PRO1 - Project, 1.5 credits, grading scale: A, B, C, D, E, FX, F
• PRO2 - Project, 1.5 credits, grading scale: A, B, C, D, E, FX, F
• TEN1 - Examination, 4.5 credits, grading scale: A, B, C, D, E, FX, 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.

### 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 SF2822

SCI/Mathematics

Mathematics

Second cycle