Optimisation NV1
Syllabus, Master's level, 1TD183
This course has been discontinued.
- Code
- 1TD183
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Computational Science A1N, Computer Science A1N
- Grading system
- Pass with distinction (5), Pass with credit (4), Pass (3), Fail (U)
- Finalised by
- The Faculty Board of Science and Technology, 3 November 2008
- Responsible department
- Department of Information Technology
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 komplementaritet for LP.
Convexity and optimality. Optimality condition for unlimited optimisation. Numerical methods for unlimited optimisation: Newton's method, most steep gradient method, and kvasi-Newtonmetoder. Methods to guarantee descentriktnigar, line increase. Non-linear least squares methods (Gauss-Newton, Levenberg-Marquard).
Numerical calculation of derivatives (finite discrepancies, automatic differentiation). Optimality condition for optimisation with constraint (KKT condition). Quadratic programs. Orientation in methods for optimisation with constraint (penalty and barrier methods, sekvensiell quadratic programming).
Instruction
Lectures and compulsory assignments.
Assessment
Written final exam and approved assignments.