Master’s studies

Syllabus for Optimisation

Optimeringsmetoder

Syllabus

  • 5 credits
  • Course code: 1TD184
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Computer Science A1N, Technology A1N, Computational Science A1N
  • Grading system: Fail (U), 3, 4, 5
  • Established: 2010-03-18
  • Established by: The Faculty Board of Science and Technology
  • Revised: 2014-05-20
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 27, 2014
  • Entry requirements: 120 credits including 30 credits in mathematics, Computer Programming I and Scientific Computing II or equivalent.
  • Responsible department: Department of Information Technology

Learning outcomes

After 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.

Content

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.

Instruction

Lectures, seminars and assignments.

Assessment

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

Reading list

Reading list

Applies from: week 27, 2014

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

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

    Find in the library

    Mandatory