Optimization, Advanced Course, 6 credits (TAOP24)

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G2X

Course offered for

• Mathematics
• Applied Physics and Electrical Engineering, M Sc in Engineering
• Computer Science, Master's programme
• Applied Physics and Electrical Engineering - International, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Introduction to optimization.

Intended learning outcomes

Optimization deals with mathematical theory and methods aiming at analyzing and solving decision problems that arise in technology, economy, medicine, etc. The course gives, together with the introductory course, a broad orientation of the field of optimization. After the course, the student shall:

• be able to identify optimization problems and classify them according to their properties, into, for example, network problems or discrete problems
• construct mathematical models of more complex optimization problems
• have knowledge about and be able to apply basic solution principles for some classes of commonly appearing optimization problems, such as, for example, the simplex method for network flows
• be able to use commonly available software for solving optimization problems that appear regularly in applications
• be able to use relaxations to approximate optimization problems and heuristic methods for finding feasible solutions, and be able to estimate the optimal objective value through lower and upper bounds
• have good knowledge about practical applications of optimization methodologies

Course content

A continuation of the material presented in the introductory course. The course includes more advanced topics within mathematical modelling, network optimization, sensitivity analysis in linear programming, discrete optimization, nonlinear optimization, and Lagrangian relaxation. Some new topics are also included, such as dynamic programming and heuristics.

Teaching and working methods

Lectures which include theory, problem solving and applications. Exercises which are intended to give individual training in problem solving. A laboratory course with emphasis on modelling and the use of optimization software.

Examination

LAB1	Laboratory course	U, G	2 credits
TEN1	Written examination	U, 3, 4, 5	4 credits

Grades

Four-grade scale, LiU, U, 3, 4, 5

Other information

Supplementary courses: Mathematical optimization.

Department

Matematiska institutionen

Director of Studies or equivalent

Ingegerd Skoglund

Examiner

Oleg Burdakov

Course website and other links

http://courses.mai.liu.se/GU/TAOP24

Education components

Preliminary scheduled hours: 38 h
Recommended self-study hours: 122 h

Course literature

Jan Lundgren, Mikael Rönnqvist & Peter Värbrand - Optimeringslära (Studentlitteratur, 2008). Jan Lundgren, Mathias Henningsson & Mikael Rönnqvist -Optimeringslära övningsbok (Studentlitteratur, 2008)