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Syllabus for

Academic year
TMA947 - Nonlinear optimisation
 
Syllabus adopted 2012-02-22 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


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 1,5c Grading: UG   1,5c    
0203 Examination 6,0c Grading: TH   6,0c   17 Dec 2013 am V,  22 Apr 2014 am V,  28 Aug 2014 am V

In programs

MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory)
MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Year 1 (compulsory elective)
TKTEM ENGINEERING MATHEMATICS, Year 3 (elective)

Examiner:

Professor  Michael Patriksson
Biträdande professor  Ann-Brith 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 optimiza-tion. 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 real-world 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 Frank-Wolfe 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 Karush-Kuhn-Tucker 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.


Published: Mon 28 Nov 2016.