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# SF1861 Optimization 6.0 credits

## About course offering

### For course offering

Spring 2025 Start 17 Mar 2025 programme students

### Target group

No information inserted

P4 (6.0 hp)

17 Mar 2025
2 Jun 2025

33%

Normal Daytime

English

KTH Campus

### Number of places

Places are not limited

## Application

### For course offering

Spring 2025 Start 17 Mar 2025 programme students

60179

## Contact

### For course offering

Spring 2025 Start 17 Mar 2025 programme students

### Contact

Per Enqvist (penqvist@kth.se)

### Examiner

No information inserted

### Course coordinator

No information inserted

### Teachers

No information inserted
Headings with content from the Course syllabus SF1861 (Autumn 2019–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

• Examples of applications of optimization and modelling training.
• Basic concepts and theory for optimization, in particular theory for convex problems.
• Linear algebra in Rn, in particular bases for the four fundamental subspaces corresponding to a given matrix, and LDLT-factorization of a symmetric positive semidefinite matrix.
• Linear optimization, including duality theory.
• Optimization of flows in networks.
• Quadratic optimization with linear equality constraints.
• Linear least squares problems, in particular minimum norm solutions.
• Unconstrained nonlinear optimization, in particular nonlinear least squares problems.
• Optimality conditions for constrained nonlinear optimization, in particular for convex problems.
• Lagrangian relaxation.

### Intended learning outcomes

After completing the course students should for a passing grade be able to

• Apply basic theory, concepts and methods, within the parts of optimization theory described by the course content, to solve problems
• Formulate simplified application problems as optimization problems and solve using software.
• Read and understand mathematical texts about for example,  linear algebra, calculus and optimization and their applications, communicate mathematical reasoning and calculations in this area, orally and in writing in such a way that they are easy to follow.

For higher grades the student should also be able to

• Explain, combine and analyze basic theory, concepts and methods within the parts of optimization theory described by the course content.

## Literature and preparations

### Specific prerequisites

Completed course in Linear Algebra, SF1624, SF1672 or SF1675.
Completed course in Multivariable Calculus, SF1626 or SF1674.

Completed course SF1668  Mathematical and numerical methods I or a course in Numerical methods corresponding to SF1668, SF1511, SF1519, SF1546 or SF1547.

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

The literature is published on the course webpage no later than four weeks before the course starts.

## Examination and completion

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

### Grading scale

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

### Examination

• HEM1 - Assignments, 1.5 credits, grading scale: P, 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.

The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented,lastingdisability. The examiner may allow another form of examination for reexamination of 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 room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

### Main field of study

Mathematics, Technology

First cycle

### Add-on studies

SF2812 Applied Linear Optimization, SF2822 Applied Nonlinear Optimization

### Contact

Per Enqvist (penqvist@kth.se)