Entry requirements

120 credits where 30 credits mathematics, Computer programming I and Scientific computing II or the equivalent is covered.

Learning outcomes

For a pass mark, the student must be able to

• formulate fundamental planning- and resource allocating problems as linear programs;
• solve small size linear programs graphically;
• explain and apply basic concepts in optimisation, e.g. 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. Linear programs, omformuleringar, graphical solutions. Algebraic and geometric properties of LP. 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, Levenberg-Marquard).

Numerical calculation of derivatives (finite differences, automatic differentiation). Optimality condition for optimisation with constraint (KKT condition). Quadratic programs. Introduction to methods for optimisation with constraint (penalty and barrier methods, sequential quadratic programming).

Instruction

Lectures and compulsory assignments.

Assessment

Written final exam and approved assignments.