Syllabus for Optimisation

Learning outcomes

After the course, the student should be able to

• formulate problems in science and engineering as optimisation problems;
• formulate fundamental optimisation problems as linear programs;
• describe and explain the principles behind algorithms covered in the course, e.g. the simplex method and quasi-Newton methods;
• 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. Linear programs, reformulations, graphical solutions. The simplex method for LP, duality and complementarity for LP.

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). Quadratic programs. Introduction to methods for optimisation with constraint (penalty and barrier methods).

Instruction

Lectures, laboratory work and assignments.

Assessment

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