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Course SF1811 Optimization

Course Description

SF1811 is a basic course on optimization.

Information per Course Offering

Termin

Autumn 2025

Information for Autumn 2025

• Start: 27 Oct 2025
• Programme students
• Course location: KTH Campus
• Duration: 27 Oct 2025 - 12 Jan 2026
• Periods: Autumn 2025: P2 (6 hp)
• Pace of study: 33%
• Application code: 50285
• Form of study: Normal Daytime
• Language of instruction: English
• Course memo: Link to course memo
• Number of places: Places are not limited
• Target group: No information inserted
• Planned modular schedule: P2: A1, D1, E1, H1, B2.
• Schedule: Link to schedule
• Part of programme:
  • Degree Programme in Energy and Environment, year 3, MHI
  • Degree Programme in Energy and Environment, year 3, HSS
  • Degree Programme in Energy and Environment, year 3, RENE
  • Master of Science in Engineering and in Education, year 5, TEDA
  • Degree Programme in Energy and Environment, year 3, SMCS
  • Degree Programme in Energy and Environment, year 3, KEM
  • Degree Programme in Energy and Environment, year 3, MES
  • Degree Programme in Energy and Environment, year 3, SUE
  • Master of Science in Engineering and in Education, year 4, TEDA
  • Degree Programme in Energy and Environment, year 3, SUT
  • Master's Programme, Computer Science, year 2, CSDA
  • Master of Science in Engineering and in Education, year 5, MAFY
  • Master's Programme, Applied and Computational Mathematics, year 1
  • Master's Programme, Machine Learning, year 1
  • Degree Programme in Engineering Mathematics, year 3, Mandatory
  • Master's Programme, Machine Learning, year 2
  • Bachelor's Programme in Information and Communication Technology, year 3
  • Master's Programme, Systems, Control and Robotics, year 2
  • Master's Programme, Systems, Control and Robotics, year 1
  • Degree Programme in Industrial Technology and Sustainability, year 3, Mandatory
  • Master's Programme, Applied and Computational Mathematics, year 2

Contact

• Examiner: Anders Forsgren
• Course coordinator: Anders Forsgren
• Teachers: Anders Forsgren

Course Syllabus

Please note: all information from the Course syllabus is available on this page in an accessible format.

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 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.

Literature

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

Examination and Completion

Grading Scale

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

Examination

• INL1 - Home assignment, 2.0 credits, grading scale: P, F
• TEN2 - Exam, 4.0 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.

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

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

Examiner

Anders Forsgren

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.

Offered By

SCI/Mathematics

Main Field of Study

Mathematics, Technology

Education Cycle

First cycle