Skip to main content
Till KTH:s startsida

SF1811 Optimization 6.0 credits

Course memo Autumn 2026-12387

Version 2 – 09/29/2026, 10:01:23 PM

Course offering

Autumn 2026-12387 (Start date 26 Oct 2026, English)

Language Of Instruction

English

Offered By

SCI/Mathematics

Course memo Autumn 2026

Headings denoted with an asterisk ( * ) is retrieved from the course syllabus version Autumn 2019

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.

Preliminary schedule

Type Day Date Time Room Subject
L1 Mon Oct 26 13-15 K1 Introduction to optimization and linear programming
(Chapters 1–3)
L2 Tue Oct 27 15-17 B2 Basic feasible solutions and the fundamental theorem of linear programming
(Chapter 4)
L3 Thu Oct 29 8-10 D2 The simplex method
(Chapter 5)
E1 Fri Oct 30 8-10 Q33, Q34 Linear programming and the simplex method
L4 Mon Nov 2 8-10 B2 Network flow and transportation problems
(Chapter 7)
L5 Wed Nov 4 8-10 B2 Duality and optimality in linear programming
(Chapter 6 and A note on linear programming optimality and duality)
E2 Mon Nov 9 10-12 W42, W43 Network flows and some linear algebra
L6 Tue Nov 10 10-12 K1 Lagrangian relaxation, duality, and sensitivity
(Chapters 6 and 22)
L7 Wed Nov 11 8-10 B2 Convex sets, convex functions, and convex optimization
(Chapters 8 and 15; selected parts of Chapters 4 and 27)
E3 Thu Nov 12 10-12 W42, W43 Duality and complementarity in LP
L8 Tue Nov 17 8-10 B2 Quadratic functions and unconstrained quadratic optimization
(Chapter 9 and selected parts of Chapter 27)
L9 Wed Nov 18 8-10 D2 Quadratic optimization with equality constraints
(Chapter 10 and selected parts of Chapter 25)
E4 Wed Nov 18 13-15 W37, W38 Quadratic programming
L10 Mon Nov 23 13-15 D2 Linear least-squares problems, orthogonal projections, and minimum-norm solutions
(Chapter 11)
L11 Tue Nov 24 8-10 B2 Unconstrained nonlinear optimization and Newton’s method
(Chapters 13–14 and 16)
E5 Wed Nov 25 13-15 W42, W43 Convex functions and Newton's method
L12 Mon Nov 30 8-10 B2 Nonlinear optimization with linear constraints: feasible directions, Lagrange multipliers, and KKT conditions
(A note on optimality conditions, Part A)
L13 Thu Dec 3 8-10 B2 Nonlinear optimization with nonlinear constraints: MFCQ and KKT conditions
(A note on optimality conditions, Part B)
E6 Thu Dec 3 15-17 W37, W38 The KKT optimality conditions
L14 Tue Dec 8 8-10 D2 Nonlinear least-squares problems and the Gauss–Newton method
(Chapter 17)
L15 Wed Dec 9 15-17 B2 Global optimality, Lagrangian relaxation, duality, and course summary
(Chapters 21–22)
E7 Thu Dec 10 8-10 W42, W43 Linear and nonlinear least-squares problems
E8 Thu Dec 10 15-17 W42, W43 Lagrangian relaxation and dual problems

Chapter references refer to the compendium by Sasane and Svanberg.

Information on exercise sessions is given in Canvas.

Preparations before course start

Literature

The main literature for the course is the compendium "Optimization" by Amol Sasane and Krister Svanberg (ASKS), which you can buy at the KTH bookstore. ASKS contains some exercises, for which solutions are available here. Additional exercises are provided in "Exercises in Optimization" (EXOPT), which is available in Canvas.

We also recommend the book Linear and Nonlinear Optimization, second edition, by I. Griva, S. G. Nash och A. Sofer, SIAM, 2009. We encourage you to buy this book, especially if you consider taking the follow-up courses SF2812 and/or SF2822, since it is used as course literature in both these courses.
(The book can be ordered from several places. Please note that you can become a SIAM student member and obtain a discount at the SIAM bookstore.)

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,lastingdisability. The examiner may allow another form of examination for reexamination of individual students.

The section below is not retrieved from the course syllabus:

INL1 – Homework assignments, 2.0 credits

The course includes three compulsory homework assignments. Each assignment may be completed individually or in a self-selected group of two students. Each group submits one written report in Canvas.

Reports submitted by the following deadlines make the members of the group eligible for bonus points on the written examinations during the academic year 2026/2027:

  • Homework assignment 1, 1 bonus point: Tuesday, 10 November 2026
  • Homework assignment 2, 1 bonus point: Tuesday, 24 November 2026
  • Homework assignment 3, 2 bonus points: Friday, 11 December 2026

A passing result for INL1 remains valid. Students who have already passed INL1 may not resubmit the homework assignments and are not eligible to earn new bonus points in a later course offering.

Regardless of bonus points, all three reports must be submitted by Friday, 11 December 2026 to be assessed in connection with the January examination. If a report submitted by this date is not accepted, the group may submit a revised report no later than the date of the January examination.

Reports may also be submitted by the date of the re-examination. A student who has not completed all three homework assignments by that date will be referred to the next course offering.

The homework assignments are intended to develop the ability to apply mathematical concepts and methods and to communicate mathematical work in writing. A report should explain the problem, provide the necessary theoretical background, and present the results at a level suitable for a student who has completed SF1811 but has not worked on the particular assignment.

The report should be written in the students' own words and should explain the main steps of the solution. The style may be similar to that used for examples in the course literature. A report will normally be no longer than five pages. The precise format is not important. The essential requirements are mathematical correctness, clarity, and sufficient explanation for the intended reader.

Any use of generative AI must be declared in the report, as described in the separate section on the use of generative AI.

TEN2 – Written examination, 4.0 credits

The written examination consists of five questions worth 10 points each, giving a maximum examination score of 50 points. Up to four bonus points from the homework assignments may be added to the examination score. A total score of at least 25 points, including bonus points, is required for a passing grade. The normal grade thresholds, including bonus points, are: E: 25 points;  D: 29 points;  C: 34 points;  B: 39 points;  A: 45 points.

One of the five examination questions assesses mathematical argumentation and understanding of theory. The question consists of two independently assessed parts: (a) formulation and proof, or derivation, of one of the announced theory results, worth 5 points; and (b) use or interpretation of the result in a related situation that is not announced in advance, worth 5 points. In part (b), the stated theory result may be used without proof.

The announced theory results and further information about the question are available in Canvas.

The grade Fx is normally given to a student who has obtained 21–24 points on the written examination itself but has not reached 25 points after bonus points have been added.

An Fx grade may be converted to an E grade through successful completion of two supplementary exercises: one concerning a theory result from the announced list and one concerning a computational or methodological part of the examination. Both exercises must be completed independently, submitted in writing, and explained orally. As in the theory question on the written examination, the oral explanation of the theory exercise includes a related part (b) that is not announced in advance.

The supplementary exercises are selected individually by the examiner based on the knowledge and skills that the student did not demonstrate sufficiently in the examination. It is the student's responsibility to contact the examiner to initiate the supplementary examination. The supplementary examination must be completed within three weeks of the date on which the student was notified of the grade.

The examination questions are written in English. Answers may be written in English or Swedish. No aids are permitted except pens, pencils, an eraser, and a ruler. Calculators and dictionaries are not permitted. The formula sheet available in Canvas will be provided with the examination.

The written examination is scheduled for Monday, 11 January 2027, 08:00–13:00. Students must register in advance in accordance with KTH's examination registration rules.

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.

Use of generative AI in the homework assignments

The homework assignments may be completed individually or in pairs. Generative AI tools may be used as support, but the submitted solution must reflect the students’ own mathematical reasoning and understanding.

AI tools may be used, for example, to discuss concepts, obtain feedback on an approach, check language, debug code, or generate plots. AI should primarily support learning and critical review. It must not replace the students’ responsibility for formulating, verifying, and presenting the final solution.

Any use of generative AI must be declared in the submission. The declaration must state:

  • which tools were used;
  • for what purposes they were used;
  • which parts of the submission were affected; and
  • how the generated material was checked, modified, or verified.

If no generative AI tool was used, this should also be stated.

For work submitted in pairs, the declaration is joint, and both students are responsible for the complete submission. Each student must be able to explain and justify all mathematical arguments, computations, code, and conclusions without AI assistance.

Declared use of generative AI does not in itself affect the assessment. The examiner or teaching assistants may ask individual oral follow-up questions to verify understanding. A submission may not be accepted if the students cannot explain or justify its contents.

Students are expected to declare their use of generative AI honestly and to the best of their knowledge. Deliberately undeclared or misrepresented use may be treated as suspected academic misconduct and handled according to KTH regulations.

Further information

No information inserted

Round Facts

Start date

26 Oct 2026

Course offering

  • Autumn 2026-12387

Language Of Instruction

English

Offered By

SCI/Mathematics

Contacts

Course Coordinator

Teachers

Examiner