Optimisation

5 credits

Syllabus, Master's level, 1TD184

A revised version of the syllabus is available.

Code: 1TD184
Education cycle: Second cycle
Main field(s) of study and in-depth level: Computational Science A1N, Computer Science A1N, Data Science A1N, Technology A1N
Grading system: Pass with distinction (5), Pass with credit (4), Pass (3), Fail (U)
Finalised by: The Faculty Board of Science and Technology, 20 May 2014
Responsible department: Department of Information Technology

Entry requirements

120 credits including 30 credits in mathematics, Computer Programming I and Scientific Computing II or equivalent.

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).