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## 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.

### Course Disposition

No information inserted

## Literature and preparations

### Specific prerequisites

Completed  course in SF1624 Linear algebra and geometry or SF1672 Linear Algebra.
Completed course in SF1626 Calculus in several variables or SF1674 Multivariable Calculus.
Completed course in Numerical analysis, SF1511, SF1519, SF1545 or  SF1546.

### Recommended prerequisites

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### Equipment

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### Literature

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## 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

• INL1 - Home assignment, 2,0 hp, betygsskala: P, F
• TEN2 - Exam, 4,0 hp, betygsskala: 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 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 SF1811

SCI/Mathematics

### Main field of study

Mathematics, Technology

First cycle