Teaching language: English
Open for exchange students
Block schedule:
X
Course module 

Credit distribution 

Examination dates 
Sp1 
Sp2 
Sp3 
Sp4 
Summer course 
No Sp 
0103 
Laboratory 
1,5 c 
Grading: UG 


1,5 c







0203 
Examination 
6,0 c 
Grading: TH 


6,0 c






17 Dec 2013 am V, 
22 Apr 2014 am V, 
28 Aug 2014 am V 
In programs
TKTEM ENGINEERING MATHEMATICS, Year 3 (elective)
MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Year 1 (compulsory elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory)
Examiner:
Professor
Michael Patriksson
Biträdande professor
AnnBrith Strömberg
Replaces
TMA946
Applied optimization
Go to Course Homepage
Eligibility:
For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.
Course specific prerequisites
Linear algebra, analysis in one and several variables
Aim
The course is an introductory course in optimization. It serves to provide (1) basic knowledge of important classes of optimization problems and application areas of optimization models and methodologies; (2) practice in describing relevant parts of a realworld problem in a mathematical optimization model; (3) knowledge of and insights into the basic mathematical theory which underlies the principles of optimality; (4) examples of optimization methods that have been and can be developed from this theory in order to solve practical optimization problems.
Learning outcomes (after completion of the course the student should be able to)
After completion of this course, the student should be knowledgeable about
the most important concepts in convex optimization, especially in convex
analysis, and those in the related areas of duality and optimality. The student
should be well aware of the basics of optimality conditions and to be able to
utilize the theory on concrete examples. The student should also know the basics
of linear optimization, especially duality, and the most ofter utilized method for
this problem class  the simplex method. Within nonlinear optimization the student
is asked to grasp the priciples behind classic methods such as steepest descent,
Newton's method, the FrankWolfe method and sequential quadratic programming,
and to have a basic knowledge about when they are expected to be convergent.
In brief, in order to pass the course the student should be able to state the KarushKuhnTucker conditions used to investigate the local optimality of a given feasible solution, and also form correct statements based on its use in concrete examples. The student should understand and be able to investigate for concrete examples basic terms such as the convexity of sets and functions. The student should be able to understand, and in particular correctly state and utilize some of the course's basic methods, in particular the simplex method, steepest descent and the most common forms of Newton methods.
Content
This basic course in optimization describes the most relevant mathematical principles that are used to analyze and solve optimization problems. The main theoretical goal is that You should understand parts of the theory of optimality, duality, and convexity, and their interrelations. In this way You will become able to analyze many types of optimization problems occuring in practice and both classify them and provide guidelines as to how they should be solved. This is the more practical goal of an otherwise mainly theoretical course.
Organisation
Lectures, exercises, two computer exercises, and a project
assignment.
Literature
An Introduction to Optimization, av N. Andreasson, A. Evgrafov och M. Patriksson, published by Studentlitteratur in 2005.
Examination
Project assignment, two computer exercises, a written exam.