SF2822 Applied Nonlinear Optimization 7.5 credits

Tillämpad ickelinjär optimering

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.

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Course information

Content and learning outcomes

Course contents *

Theory and methods:

Newton methods, Quasi-Newton methods, and conjugate-gradient methods for unconstrained optimization. Optimality conditions, quadratic programming, SQP methods, and primal-dual interior methods for nonlinearly constrained optimization. Semidefinite programming and interior methods. Convexity and convex relaxations.


This part of the course consists of modeling practical optimization problems and using available optimization software to solve them. The projects are carried out in small groups. An important aspect of the course is cooperation within the group as well as presentations in talking and in writing.

Intended learning outcomes *

To deepen and broaden the student's theoretical and methodological knowledge in nonlinear programming.

To give training in the art of modeling and solving practical problems, and in presenting the results.

Course Disposition

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Literature and preparations

Specific prerequisites *

In general:

150 university credits (hp) including 28 hp in Mathematics,  6 hp in Mathematical Statistics and 6 hp in Optimization. Documented proficiency in English corresponding to English B.

More precisely for KTH students:

Passed courses in calculus, linear algebra, differential equations, mathematical statistics, numerical analysis, optimization. A passed second course in numerical analysis is an advantage.

Recommended prerequisites

The prerequisites is a Swedish or foreign degree equivalent to Bachelor of Science of 180 ECTS credits, with at least 45 ECTS credits in mathematics. The students should have documented knowledge corresponding to basic university courses in analysis, linear algebra, numerical analysis, differential equations and transforms, mathematical statistics, and optimization.


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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

Grading scale *

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.

Other requirements for final grade *

A written exam (TEN1; 4,5 hp).
Projects (PRO1; 3 hp).

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Anders Forsgren

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

Offered by


Main field of study *


Education cycle *

Second cycle

Add-on studies

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Anders Forsgren (andersf@kth.se)

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.