Syllabus for Optimisation



  • 5 credits
  • Course code: 1TD184
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Computer Science A1N, Data Science A1N, Technology A1N, Computational Science A1N

    Explanation of codes

    The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:

    First cycle

    • G1N: has only upper-secondary level entry requirements
    • G1F: has less than 60 credits in first-cycle course/s as entry requirements
    • G1E: contains specially designed degree project for Higher Education Diploma
    • G2F: has at least 60 credits in first-cycle course/s as entry requirements
    • G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
    • GXX: in-depth level of the course cannot be classified

    Second cycle

    • A1N: has only first-cycle course/s as entry requirements
    • A1F: has second-cycle course/s as entry requirements
    • A1E: contains degree project for Master of Arts/Master of Science (60 credits)
    • A2E: contains degree project for Master of Arts/Master of Science (120 credits)
    • AXX: in-depth level of the course cannot be classified

  • Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
  • Established: 2010-03-18
  • Established by:
  • Revised: 2022-10-18
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: Autumn 2023
  • Entry requirements:

    120 credits including 30 credits in mathematics of which 5 credits mathematics containing several variable calculus that can be taken in parallel. Computer Programming I. Participation in one of the courses Scientific Computing basic course, Scientific Computing I, Scientific Computing Bridging course or Numerical methods and Simulation. Proficiency in English equivalent to the Swedish upper secondary course English 6.

  • Responsible department: Department of Information Technology

Learning outcomes

On completion of the course, the student should be able to:

  • formulate problems in science and engineering as optimisation problems;
  • describe and explain the principles behind algorithms covered in the course;
  • explain and apply basic concepts in optimisation, such as convexity, basic solutions, extreme values, duality, convergence rate, Lagrangian, KKT conditions;
  • choose appropriate numerical method for different classes of optimisation problems using the methods advantages and limitations as a starting-point;
  • choose and use software for solving optimisation problems.


Examples of optimisation problems in operations research and for technical, scientific and financial applications. Formulating optimisation problems arising form these application areas. .

Convexity and optimality. Optimality condition for unlimited optimisation. Numerical methods for unlimited optimisation: Newton's method, Steepest descent method, and quasi-Newton methods. Methods to guarantee descent directions, line search. Non-linear least squares methods (Gauss-Newton).

Optimality condition for optimisation with constraint (KKT condition). Introduction to methods for optimisation with constraints (penalty and barrier methods, Simplex method). Duality and complementarity.

The software used in the course is MATLAB and MATLAB optimisation toolbox.


Lectures, seminars and assignments.


Written exam (3 credits) and assignments (2 credits).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Reading list

Reading list

Applies from: Autumn 2023

Some titles may be available electronically through the University library.

  • Griva, Igor.; Nash, Stephen; Sofer, Ariela Linear and nonlinear optimization

    2nd ed.: Philadelphia: Society for Industrial and Applied Mathematics, c2009

    Find in the library