Syllabus

Optimization NV1

7.5 credits

Course code: 1TD183
Established: 2007-03-15
Established by: Teknisk-naturvetenskapliga fakultetsnämnden
Revised: 2009-04-20
Requirements: 120 ECTS credits where 30 ECTS credits mathematics, Computer programming I and Scientific computing II or the equivalent is covered.
Level of education: Advanced level
Grading System: U Fail, 3 Pass, 4 Pass with credit, 5 Pass with distinction

Main Area of Studies
Computational Science, Computer Science

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 optimization, e.g. convexity, basic solutions, extreme values, duality, convergence rate, Lagrangian, KKT conditions;
  
• choose appropriate numerical method for different classes of optimization problems using the methods advantages and limitations as a starting-point;
  
• choose and use software for solving optimization problems.
  

Contents

Examples of optimization 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).

Instructions

Lectures and compulsory assignments.

Examination

Written final exam and approved assignments.