Introduction to Optimization, 6 credits (TAOP07)

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

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

Calculus, linear algebra, and Matlab

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 a broad orientation of the field of optimization, with emphasis on basic theory and methods for continuous and discrete optimization problems in finite dimension, and it also gives some insight into its use for analyzing practical optimization problems. After the course, the student shall be able to:

• identify optimization problems and classify them according to their properties, into, for example, linear and nonlinear, or continuous and discrete, problems
• construct mathematical models of simple optimization problems
• define and use basic concepts, such as, for example, local and global optimality, convexity, weak and strong duality, and valid inequalities
• reproduce and apply basic theory for some common types of optimization problems, such as, for example, duality theory for linear optimization problems, and have knowledge about and be able to use optimality conditions, such as, for example, Bellman's equations, to determine the optimality of a given solution
• describe and apply basic principles for solving some common types of optimization problems, such as, for example, branch-and-bound for discrete problems
• use relaxations, and especially Lagrangian duality, to approximate optimization problems, and be able to estimate the optimal objective value through lower and upper bounds
• use commonly available software for solving optimization problems of standard type.

Course content

Fundamental concepts within optimization, such as mathematical modelling, optimality conditions, convexity, sensitivity analysis, duality, and Lagrangean relaxation. Basic theory and methods for linear and nonlinear optimization, and integer and network optimization.

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 Work	U, G	1 credits
TEN1	Written examination	U, 3, 4, 5	5 credits

Grades

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

Other information

Supplementary courses: Optimization, advanced course Y, Applied optimization - project course, Mathematical optimization.

Department

Matematiska institutionen

Director of Studies or equivalent

Ingegerd Skoglund

Examiner

Torbjörn Larsson

Course website and other links

http://courses.mai.liu.se/GU/TAOP07

Education components

Preliminary scheduled hours: 60 h
Recommended self-study hours: 100 h

Course literature

Jan Lundgren, Mikael Rönnqvist och Peter Värbrand: Optimeringslära (Studentlitteratur). Exempelsamling: Optimeringslära grk för Y.