Course syllabus

# Optimering Optimization

## FMA051, 6 credits, A (Second Cycle)

Valid for: 2014/15
Decided by: Education Board B
Date of Decision: 2014-04-08

## General Information

Main field: Technology.
Elective Compulsory for: I3
Elective for: BME4, D4, E4, F4, F4-bs, F4-fm, F4-r, Pi3-bs, Pi3-fm, Pi4-bg, Pi4-bem
Language of instruction: The course will be given in English on demand

## Aim

The aim of the course is to present basic optimization theory, and to give an overview of the most important methods and their practical use.

## Learning outcomes

Knowledge and understanding
For a passing grade the student must

be familiar with and, in his/her own words, be able to describe the optimization algorithms, for problems with and without constraints, encountered in the course, and their properties.

be familiar with the theory of convex sets and convex functions, and be able to state and derive the most important theorems on convexity.

be aware of how to make use of convexity in the treatment of an optimization problem.

be familiar with Kuhn-Tucker Theory and be able to state and derive the most important theorems therein.

Competences and skills
For a passing grade the student must

be able to demonstrate an ability to solve optimization problems within the framework of the course.

be able to demonstrate an ability to handle optimization problems using a computer.

be able to demonstrate an ability to, in the context of problem solving, develop the theory somewhat further.

be able to describe the connections between different concepts in the course, with proper terminology and in a well structured and logically consistent manner,.

with proper terminology, suitable notation, in a well structured way and with clear logic be able to describe the solution to a mathematical problem and the theory within the framework of the course.

## Contents

Quadratic forms and matrix factorisation. Convexity. The theory of optimization with and without constraints: Lagrange functions, Kuhn-Tucker theory. Duality. Methods for optimization without constraints: line search, steepest descent, Newton methods, conjugate directions, non-linear least squares optimization. Methods for optimization with constraints: linear optimization, the simplex method, quadratic programming, penalty and barrier methods.

## Examination details

Grading scale: TH
Assessment: Written test comprising theory and problems. Two computer exercises and one project.

Parts
Code: 0196. Name: Optimization.
Credits: 6. Grading scale: TH.
Code: 0296. Name: Computer Programming.
Credits: 0. Grading scale: UG.

## Admission

Required prior knowledge: Basic university studies in calculus and linear algebra, including basic theory of quadratic forms.
The number of participants is limited to: No

## Reading list

• Lars-Christer Böiers: Mathematical Methods of Optimization. Studentlitteratur, 2010, ISBN: 978-91-44-07075-9.
• Computer Laboratory Exercises in Optimization. Provided by the department.

## Contact and other information

Course coordinator: Studierektor Anders Holst, Studierektor@math.lth.se
Course homepage: http://www.maths.lth.se/course/opt/