Optimization
MATC61 Optimization, 7.5 credits, is an elective course at upper basic level for a Bachelor or Master of Science degree in mathematics at the Faculty of Science. The course is given by the Department of Mathematics at the Faculty of Engineering (with the course code FMAN61). The course is given at half-study pace during the second half of the autumn semester. The course is given in English.
Course Content
- Quadratic forms and matrix factorisation. Convexity. Separating planes and Farkas' Lemma.
- The theory of optimization with and without constraints: Lagrange functions.
- Karush-Kuhn-Tucker theory. Duality.
- Introduction to methods for optimization without constraints: line search, steepest descent, Newton methods, conjugate directions, non-linear least squares optimization.
- The Nelder-Mead search algorithm without derivatives.
- Introduction to methods with constraints: linear optimization, quadratic programming, penalty and barrier methods.
Teaching
The teaching consists of lectures, seminars, exercises, computer exercises and a programming assignment that should be completed during the course. The programming assignment consists of a couple of given optimization problems that the student must solve by writing a computer program. The student must present and evaluate the results in a written report. Participation in computer exercises and programming assignment and thereby integrated teaching is compulsory.
Assessment
The examination takes place in the form of a written exam covering theory and problems at the end of the course, two compulsory computer exercises during the course and a programming assignment with an appurtenant written report.
Course Literature
- Stefan Diehl, Optimization, Studentlitteratur, to appear
- (L.-C. Böiers, Mathematical Methods of Optimization, Studentlitteratur, 2010, old course literature)
Official Course Description
Course Evaluation
Link to course evaluations on the department's website: