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Graduate courses

Departments' graduate courses for PhD-students.

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Syllabus for

Academic year
TMA947 - Nonlinear optimisation  
Olinjär optimering
 
Syllabus adopted 2019-02-22 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: Second-cycle
Major subject: Software Engineering, Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English
Application code: 20123
Open for exchange students: Yes

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   29 Oct 2020 am J   02 Jan 2021 am J   17 Aug 2021 am J  

In programs

MPDSC DATA SCIENCE AND AI, MSC PROGR, Year 1 (compulsory)
TKTEM ENGINEERING MATHEMATICS, Year 3 (elective)
MPCAS COMPLEX ADAPTIVE SYSTEMS, MSC PROGR, Year 1 (compulsory elective)
MPCAS COMPLEX ADAPTIVE SYSTEMS, MSC PROGR, Year 2 (elective)
MPCOM COMMUNICATION ENGINEERING, MSC PROGR, Year 2 (elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory)
MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Year 2 (elective)
MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Year 1 (compulsory elective)

Examiner:

Ann-Brith Strömberg

  Go to Course Homepage


Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

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)

Master the most important basic concepts in convex optimization, especially in convex
analysis, and those in the related areas of duality and optimality. 

Be well aware of the basics of necessary and sufficient optimality conditions and be able to
utilize this theory on concrete examples. 

Master the basics
of linear optimization, especially within duality theory, and the most often utilized method for
this problem class: the simplex method. 

Within nonlinear optimization master the notions of descent and feasible direction, and to be able to explain the principles behind classic methods such as steepest descent, variations of Newton's method, the Frank-Wolfe method, and sequential quadratic programming,
and to be able to explain when they are expected to be convergent.



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 occurring 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 comprising mathematical modelling and the solution of a concrete optimization problem med industrial relevance. Additionally, there is a voluntary "master class" geared towards more advanced topics.

Literature

"An Introduction to Contimuous Optimization", by Niclas Andréasson, Anton Evgrafov och Michael Patriksson, med Emil Gustavsson, Zuzana Nedelkova, Kin Cheong Sou och Magnus Önnheim, third edition published by Studentlitteratur in 2016.

Examination including compulsory elements

Project assignment, two computer exercises, a written exam. An active participation in a (voluntary) master class can yield up to two additional points towards a higher degree than pass on the first written exam.


Page manager Published: Thu 04 Feb 2021.