Syllabus for Optimisation

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.

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).

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.